Benchmarking econometric, decomposable additive, and neural network methods for food inflation prediction featuring policy insights PDF Free Download
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Benchmarking econometric,
decomposable additive, and neural
network methods for food ination
prediction featuring policy insights
Abu Javed
With a longstanding struggle to achieve food self-suciency, Bangladesh is facing a severe food
security crisis, as highlighted by its placement on the World Bank’s “Red List” for food ination for
two consecutive years. Both the World Bank and the Bangladesh Bureau of Statistics (BBS) conrm
that food ination has exceeded 10% over the past year. The crisis of rising food costs, attributed
to a combination of global, local, and structural issues, is exacerbating socioeconomic hardships for
low-income households. It necessitated an in-depth investigation into the external factors inuencing
food ination at the domestic level, acknowledging that unprecedented ination is one of the biggest
hindrances to economic growth and development. Existing research on food ination is extensive, yet
the majority of these studies employ statistical/econometric models and fail to produce comparative
analyses. Seeking to address this gap, the author analyzed the combined impact of climate variables
and the Energy Price Index on the Food Price Index, employing machine learning models with monthly
data of Bangladesh from July 2010 to March 2025. The study proposed four distinct time series models:
SARIMAX, TDANN, Prophet, and LSTM. Out of all the tested models, with the lowest error metrics
(RMSE and MAE), ANN [6] stood as the best, supporting the hypothesis of this research that nonlinear
ML models are better at predicting food ination than the traditional models. Based on the key
ndings from Explainable AI (SHAP) and decomposed Prophet component analysis, the study presents
solid, instantaneous focus-based policy implications for the agricultural input and energy markets,
addressing problems from both sides to better manage uncertainty during weather shocks and energy
price volatility. The study can serve as a reliable reference for researchers and policymakers to inform
strategies for mitigating the ongoing food security crisis in Bangladesh.
Food ination is arguably one of the most concerning phenomena, a catalyst driving the macroeconomic forces
in any developing country in the world, and Bangladesh is no exception. Currently, in this age of globalization,
where economies are interconnected under the same sky, the rising price of common consumer food is a global
issue. Since its inception in 1971, Bangladesh has taken small steps to ght poverty and raise its living standards
despite minimal international support. Due to a lack of technology, inadequate mass production, and a shortage
of agricultural resources, coupled with natural disasters, a new state had to build everything brick by brick to
ght its way out of low-income status. As a result, towards the end of 1980, Bangladesh had started to face the
pressure of ination1.
Bangladesh experienced a period of moderate ination in the 1990 s and early 2000 s, averaging less than 4%.
However, ination rose sharply to a two-digit level in 2007-08, reaching a high of 12.28%. is was primarily
driven by a signicant surge in food ination, which was 16.69% in 2007-08, and was particularly severe for
rural households. Aer a brief decline, ination surged again in 2010-11, reaching 10.89% with food ination at
14.09%2. In the latest Food Security Update of June 13, Bangladesh is on the “Red List” by the food price ination
tracker for having a double-digit food ination rate of over 10% for two consecutive years3.
Food ination has historically accounted for the majority of ination in Bangladesh since people’s
consumption of food makes up a signicant portion of their overall consumption basket4. In recent times, the
outbreak of COVID-19 and the subsequent Russia-Ukraine war have signicantly increased ination, especially
food ination, posing challenges to macroeconomic stability in Bangladesh5.
Department of Economics, Bangladesh University of Professionals, Dhaka, Bangladesh. email:
abujaved.aj@gmail.com
OPEN
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Acknowledging unprecedented ination in food prices as one of the biggest hindrances in the path of
economic growth and development, this research dives into understanding the explanatory factors causing
it. For cogent policy suggestions towards curbing inationary pressure, it is imperative to review food price
ination from various aspects.
In a study by Brown and Kshirsagar6, in which they modeled the impact of weather disturbances on local
food aordability, food prices from 554 local markets in 51 countries were examined from 2008 and 2012, and
almost 20% of local market prices were aected by domestic weather disturbances. A study focusing on ve large
countries in the region, namely Bangladesh, India, Nepal, Pakistan, and Sri Lanka, suggests that there is likely
to be a signicant negative impact on food production and prices in all South Asian countries due to changes in
agricultural productivity induced by climate change7.
Melo-Velandia et al.8 estimated a non-stationary extreme value model for Colombian food prices, and the
ndings suggest that perishable foods are more exposed to extreme weather conditions compared to processed
foods. In fact, an extremely low precipitation level only explains high prices in perishable foods. e risk of high
prices for perishable foods is signicantly higher for low rainfall levels (dry seasons) compared to high rainfall
levels (rainy seasons).
Intergovernmental Panel on Climate Change (IPCC) reports that the average air temperature at the end of
the 21 st century will increase by 4.0 (
◦
C) from current levels, according to the fossil energy intensive scenario,
and as a result, agricultural production will be aected by global warming through changes in yields and market
prices9.
Interestingly,Lee10 found that while weather shocks temporarily raise consumer prices, especially for fresh
food, their eect on core prices is marginal. Among various types of weather shocks, precipitation has a greater
impact on prices compared to temperature, especially during summer. A study11, using dynamic panel estimation
across 34 OECD economies from 1985-2010, reveals precipitation has signicant nonlinear eects on food CPI
ination. Both very low and very high precipitation levels increase food CPI ination. Interestingly, temperature
shows no additional explanatory power for food CPI ination beyond what precipitation explains.
On the contrary,Chowdhury et al.12 found from the NARDL evidence and time frequency wavelet approaches
that the relationship between energy and food prices is characterized by its nonlinear and asymmetric nature.
In the long term, both increases and decreases in energy prices inuence food prices. Notably, an escalation
in energy prices exerts a more signicant and enduring impact on food prices compared to a reduction.
Furthermore, energy prices serve as a leading indicator for wheat and corn prices, preceding their movements
by a substantial 16 months.
A study specically examined the impact of temperature variations on rice productivity, the most common
staple food in Bangladesh, using parametric and nonparametric methods: K-means clustering, wavelet coherence
analysis, and regression analysis. It reveals that temperature variability has a signicant impact on rice production
across seasons and regions, directly aecting the supply and potentially the price of rice13.Alam et al.14 analyzed
long-term climate trends and their implications for rice yield, concluding that climate variability accounts for a
substantial portion of crop yield variability, with maximum temperature and rainfall having a signicant impact
on rice yields by using linear regression model. Using the dynamic computable general equilibrium (CGE)
model a study15 examined the eects of climate change by taking into account the changes in temperature and
precipitation over time and found that the impacts of climate change on rice sectors were intense, increasing
prices by 5.82% and 8.11%, reducing output by −3.08% and −3.7% collectively in 2030 and 2050 in Bangladesh.
e availability and aordability of various forms of energy play a vital role in determining the general price
level of food in Bangladesh, both in the short and long term. Oil prices signicantly impact food costs, with
agricultural food prices rising in response to any oil price shock. In fact, oil price uctuations account for 64.17%
of the variation in food prices16. is strong link means that oil price ination not only jeopardizes energy
security but also poses a threat to food security, highlighting the critical need to diversify energy sources within
the agricultural sector of South Asian economies including Bangladesh.Alauddin et al.17 employed the NARDL
model and it revealed that the change in oil prices asymmetrically impacts food price ination only in the short
run. A policy brief18 highlights that increases in international petrol prices oen lead to upward adjustments
in domestic fuel costs, with diesel’s volatility having a major impact on both food and non-food ination in
Bangladesh. e rise in diesel prices, following the Russia-Ukraine War, notably increased consumer spending
by an estimated 13.19% on non-food items and 17.4% on food items. While long-term impacts are less clear-cut,
the initial fuel price increases tend to persist over time.
Research objectives
Accurate food price index forecasting is critical for various stakeholders, including food producers, consumers,
and policymakers, enabling informed decision-making, risk management, and optimal resource allocation.
Food price indices are inherently complex, exhibiting non-linear relationships, volatility, and strong temporal
dependencies inuenced by a multitude of factors such as supply-demand dynamics, geopolitical events, weather
conditions, and economic indicators. Traditional linear forecasting models oen fall short in capturing these
intricate patterns. Despite numerous investigations of the impacts of miscellaneous factors on food prices or
food ination, these have been studied in the past; predictive analysis of food prices at the domestic level using
machine learning methods combining both climate and energy indicators is still scarce.
e primary objectives of this study are:
• To explore the factors behind the general food price level by utilizing multiple machine learning and time
series predictive models.
• To understand the forces/features impacting the historical changes in food price ination in Bangladesh using
XAI (SHAP) for better policy interventions.
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• To establish a comparative analysis among the best-performing models with a view to nding the ideal model
and providing suggestions for superior forecast accuracy.
• To demystify the delayed eects on current data, incorporate established knowledge from agricultural and
non-agricultural markets, the duality of energy costs, and weather shocks to strengthen the bridge between
policy implications and interventions in economic literature.
is paper emphasizes a Time-Delay Articial Neural Network (TDANN) model19,20 specically a Nonlinear
Autoregressive with Exogenous Inputs (NARX)-like architecture, and a deep learning model, Long Short-Term
Memory (LSTM) networks21, to address the challenges of food price index prediction by leveraging their capacity
for nonlinear mapping and sequential data processing. Additionally, another standard ML model, Prophet, has
been developed, utilizing the same data to compare its performance with that of the TDANN models.
Hypotheses for the study
In a recent study by Rana22, it was found that rising climate risks have become the biggest obstacle to attaining
the Sustainable Development Goals (SDGs) in South Asia. Risks related to extreme heat, water scarcity, and
urban heat islands disrupt critical systems, such as agriculture, energy, and public health, which are essential
for maintaining the food production and supply chain. e study also suggests that taking adaptive measures
to mitigate the impacts of extreme heat is paramount. Erratic land surface temperature and heating degrees can
both positively and negatively impact the state of food security and sustainable agriculture, which is associated
with the second goal (Zero Hunger) of the SDGs23. A recent paper also highlights the importance of renewable
energy consumption for environmental management and sustainability24. e studies aided in having condence
in variable selection for sharpening the research focus and policy implications.
Previous literature has provided strong justication for taking a nonlinear machine learning approach to
model the chosen variables of this study and dissect the ambiguous eects of lags among the internal variables
to explain temporal dependencies. In recent studies, Machine Learning (ML) techniques have been producing
promising results in modeling time series data, specically in forecasting food prices, outperforming traditional
models25,26. e diverse modeling suite allows for comprehensive prediction and factor exploration, establishing
robust benchmarks for forecasting accuracy.
Bangladesh’s persistent struggle for food self-suciency, highlighted by its placement on the World Bank’s
Red List for consecutive years due to food ination exceeding 10%, underscores a severe, multifaceted crisis.
is escalating cost, driven by structural, local, and global forces, is severely impacting low-income households
and hindering national economic progress. While extensive research exists on food ination, a signicant gap
remains in studies that provide comparative analyses and link key external drivers directly to domestic policy
levers. To address this, this study proposes a new, data-driven investigation. First, a domestic-level Bangladesh
model is sought that uniquely combines the eects of climate variables (capturing weather shocks) and the Energy
Price Index (representing input cost volatility) on the Food Price Index. Second, the research oers a rigorous
comparative analysis of four advanced forecasting models, all evaluated on the same monthly data spanning July
2010 to March 2025, that present elements to clarify the temporal eects. Finally, and most critically, the core
contribution lies in the application of Explainable AI (XAI), specically SHAP (SHapley Additive exPlanations),
to decode the models. is analysis moves beyond raw prediction by providing actionable, quantitative insights
into which forces (features) historically impact food price ination, directly supporting better, evidence-based
policy interventions. e research culminates in a comparative analysis to isolate the ideal predictive model,
providing concrete suggestions for achieving superior and reliable forecast accuracy in the long term.
So, this paper aims to hypothesize whether the non-linear research approach using machine learning models
produces better results than the traditional linear approach in detecting the volatile movements of food ination.
e author will also inspect whether the comparative analysis among the proposed models yields similar results
or not. Additionally, this study seeks to identify which models better explain the underlying dynamics of the
food industry by delving deep into the impacts of agricultural, non-agricultural, and climate risk features or
factors.
Methods
Data sources and preprocessing
For statistical analyses and modeling of the neural networks, ve time series variables are selected based
on previous literature, in line with the research objectives. Among these variables, three are weather factors
representing climate indicators termed as temperature anomalies by month, monthly average surface
temperatures, and monthly precipitation. To account for the price volatility of electricity, natural gas, coal, fuel,
and miscellaneous liquid resources, the energy price index is considered a quintessential input factor, while the
food price index is the output of the neural network models (Table 1). As the focus is on building predictive
models on the price level of food items at the country level, the food price index is regarded an ideal indicator
rather than considering the consumer price index. Descriptive statistics are shown in Table 2, composed of
exploratory data analysis (EDA) elements such as standard deviation, mean, median, range, etc.
All input variables, including output, are collected from highly reliable and authentic secondary sources.
Every input and output data are seasonal in nature, spanning from July 2010 to March 2025, having 177 entries
in total, and were sourced from World Bank Data Indicators, Our World in Data repositories and Copernicus
Climate Data Store (CDS). e nal data set for modeling and evaluation was created by cleanly merging and
labeling them for convenience (Fig. 1).
en, a correlation analysis is performed to see the underlying linear relationships among the multiple
variables within a dataset. e correlation coecient shows the strength of the linear association between two
variables. In this preprocessing stage, the correlation matrix is visualized with the cor and corrplot functions
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60 80 100 120 140
Food Price Index
18 20 22 24 26 28 30
Monthly Average Surface Temperatures (°C)
60 80 100 120
2010 2015 2020 2025
Energy Price Index
Time
−1 012
Temperature Anomalies by Month (°C)
0 100 200 300 400 500 600 700
2010 2015 2020 2025
Monthly Precipitation
Time
Timeseries Data for the Models: Key Features & Distributions
Fig. 1. Key features and distributions of the timeseries dataset (July 2010 - March 2025) | Source: World
Development Indicators − DataBank, Our World in Data, and Copernicus Climate Data Store [2025].
Variable nMean SD Median Trimmed Min Max Range Skew Kurtosis SE
Food Price Index 177 82.18 23.01 79.82 80.34 46.89 139.58 92.69 0.58 −0.54 1.73
Monthly Average Surface Temperatures (
◦
C) 177 25.58 3.98 27.45 26.01 16.72 30.34 13.62 −0.79 −0.84 0.3
Energy Price Index 177 87.97 19.53 87 87.1 56.7 132.1 75.4 0.32 −0.7 1.47
Temperature Anomalies by Month (
◦
C) 177 0.26 0.68 0.31 0.29 −1.6 2.52 4.12 −0.34 0.34 0.05
Monthly Precipitation 177 171.72 159 141.27 156.79 0.48 687 686.53 0.58 −0.67 11.95
Table 2. Descriptive statistics.
Period Variable name Unit Frequency Purpose Description Source
July 2010
- March
2025 Food Price Index Monthly Output e change in retail prices that consumers in a specic country pay for a basket
of food and beverages. It’s a key component of the overall Consumer Price
Index (CPI). World Bank27
July 2010
- March
2025
Monthly
Average Surface
Temperatures
(
◦
C)
Celsius Monthly Input e temperature of the air measured 2 meters above the ground, encompassing
land, sea, and in-land water surfaces, measured in degrees Celsius.
Contains modied
Copernicus Climate
Change Service
information28
July 2010
- March
2025
Energy Price
Index Monthly Input e change in retail prices that consumers pay for a basket of energy sources,
such as electricity, gasoline, and natural gas. It’s a critical component of a
country’s Consumer Price Index (CPI). World Bank27
July 2010
- March
2025
Temperature
Anomalies by
Month (
◦
C) Celsius Monthly Input e dierence in a specic month’s average surface temperature from the mean
temperature of the same month during the period 2010-2025, measured in
degrees Celsius.
Contains modied
Copernicus Climate
Change Service
information29
July 2010
- March
2024
Monthly
Precipitation Millimeters Monthly Input Total annual precipitation-rain and snow-calculated as the sum of daily
averages, reported as the depth of water falling to Earth’s surface, excluding fog
and dew.
Contains modied
Copernicus Climate
Change Service
information30
Table 1. Data description with source.
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of R, with the range between +1 and −131. Any score nearing +1 means a positive linear relationship, and any
score nearing −1 means a negative linear relationship (Fig. 2). Although multicollinearity is not an issue for the
robustness and overparameterization of the ANN models, correlation analysis is valuable for a complete EDA
picture. Histograms with density curves showed that variables were not normally distributed (Fig. 3).
However, further processing was necessary. Min-max normalization, also known as scaling to a range, a data
preprocessing technique, was used to transform the variables to a specic range, typically between 0 and 1. e
preProcess function within the caret package was employed32. It’s one of the simplest and most common ways
to normalize data. Many machine learning algorithms, like neural networks, are sensitive to the scale of input
features. If the ranges of features dier signicantly from each other, the algorithm might give more weight to
features with a greater spread, leading to biased results or slower convergence. Normalization ensures that all the
features are leveled to the same range and can contribute fairly.
e entire data analysis process, from data pre-processing to model evaluation, including feature importance,
is carried out using the statistical soware R, version 4.4.333 and Python, version 3.13.5.
SARIMAX: a baseline framework
e Seasonal Autoregressive Integrated Moving Average with Exogenous Regressors (SARIMAX) model is a
powerful time series forecasting technique that signicantly extends the basic ARIMA model’s capabilities. It’s
formally denoted as
SARIMAX(p, d, q)(P,D,Q)m
, where the non-seasonal components (p, d, q) handle
the Autoregressive, Dierencing (Integration order d for non-stationarity), and Moving Average aspects,
respectively. Simultaneously, the dedicated Seasonal structure (P, D, Q) captures cyclical patterns over a cycle
length m, addressing Seasonal Autoregressive, Seasonal Dierencing, and Seasonal Moving Average components.
Crucially, the model’s inclusion of exogenous regressors allows it to incorporate and quantify the inuence of
other independent variables on the forecast, providing a comprehensive framework for complex time series
analysis34.
e general form of the
SARIMAX(p, d, q)(P,D,Q)m
model is:
Φ
P(Bm)ϕp(B)(1 −B)d(1 −Bm)Dyt=Θ
Q(Bm)θq(B)ϵt+
k
∑
i=1
βixi,t (1)
1.00
0.01
0.99
0.31
−0.05
0.01
1.00
0.01
0.42
0.74
0.99
0.01
1.00
0.31
−0.05
0.31
0.42
0.31
1.00
0.10
−0.05
0.74
−0.05
0.10
1.00
−1
−0.7
5
−0.5
−0.2
5
0
0.25
0.5
0.75
1
Food Price Index
Monthly Average Surface Te
mperatures (°C)
Energy Price Index
Temperature Anomalies by Month (°C)
Monthly Precipitation
Food Price Index
Monthly
Average Surface Temperatures (°C)
Energy Price Index
Temperature Anomalies by Month (°C)
Monthly Precipitation
Fig. 2. Pearson correlation matrix of original 5 features from the nal dataset.
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Where:
•
ϕp(B)
and
ΦP(Bm)
are the non-seasonal and seasonal AR polynomials.
•
θq(B)
and
ΘQ(Bm)
are the non-seasonal and seasonal MA polynomials.
•
(1 −B)d
and
(1 −Bm)D
apply the non-seasonal and seasonal dierencing to make the series stationary.
•
ϵt
is the white noise error term (residuals).
•
∑k
i=1
β
i
x
i,t
is the linear combination of k exogenous regressors
xi,t
with corresponding coecients
βi
.
Articial Neural Network (ANN)
An Articial Neural Network (ANN) model draws its fundamental inspiration from the biological neural
networks of the human brain. e core idea is to create a computational system that learns and processes
information in a manner analogous to how a real human brain operates by learning from neural synapses. e
historical concept dates back to the 1940 s with prototype models such as the McCulloch-Pitts neuron, pioneering
the groundwork of neural network models popular in academic research and science35. e Perceptron in the
late 1950 s was a signicant step that could learn simple patterns, but the real revolutionary invention emerged
with the development of the backpropagation algorithm in the 1980 s, as it introduced the method of training
multi-layered networks to achieve precision in computational accuracy. At the core of any ANN, the blueprint is
derived as the interconnected nodes segmented into dierent layers, receive information as input, and produce
output as nal results.
ANN models are potent tools to explore pattern recognition, classication, and regression analysis, adept
at building complex and especially non-linear relationships within data of any category. In general, an ANN
comprises three major layers of neurons, or more technically, nodes. Primarily, nodes are placed in three main
layers: input, hidden, and output functions, with associated weights by the optimization phase of the modeling.
is study used the Resilient Backpropagation (RPROP) algorithm36, which is generally faster and more robust
than traditional backpropagation because it uses only the sign of the gradient to determine the weight update,
rather than the magnitude. is makes it less sensitive to the learning rate hyperparameter and helps avoid issues
like slow convergence or getting stuck in local minima37. Neurons work by computing a weighted sum of their
inputs, adding a bias term for each layer, and passing through an activation function. Mathematically, the output
yj
of a neuron j can be expressed as:
(A)
Food Price Index
Density
40 60 80 100120 140
0.000 0.0050.010 0.015
(B)
Monthly Average Surface Temperatures (°C)
Density
20 25 30
0.00 0.05 0.10 0.15 0.20
(C)
Energy Price Index
Density
60 80 100 120 140
0.000 0.005 0.0100.015 0.020
(D)
Temperature Anomalies by Month (°C)
Density
−2 −1 0123
0.00.1 0.20.3 0.40.5
(E)
Monthly Precipitation
Density
0100 200300 400 500 600 700
0.0000.001 0.0020.003 0.004
Fig. 3. Histograms of the timeseries inputs and output with density curves.
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y
j=α
(n
∑
i=1
wjixi+bj
)
(2)
where
xi
are the inputs from the previous layer,
wji
are the weights connecting input i to neuron j,
bj
is the bias
for neuron j, and
α(·)
is the activation function38.
Time-delay architecture for time series forecasting
Feature selection
e selection of appropriate lag values is susceptible to the model t and the model’s overall performance.
Consequently, the number of lags in the input data determines the total number of input features for an ML
model like TDANN. Using fewer lags reduces the number of parameters the model has to learn. is strategy
makes it less prone to overtting, where the model learns noise or specic patterns from the training data that
don’t generalize to new data.
In Fig. 4a, the cross-correlation analysis examined temporal dependencies between the Food Price Index and
its predictors. e Food Price Index showed strong autocorrelation at lag 3, supporting its inclusion as a lagged
input. Monthly Average Surface Temperatures (
◦
C) did not exhibit statistically signicant cross-correlations,
suggesting limited direct short-term inuence. e Energy Price Index displayed strong correlations at lags 0,
1, 2 and 3, reecting both current and immediate past eects. Temperature Anomalies by Month (
◦
C) showed
moderate correlation at lags 0, 1, 2, 3 and 4, while Monthly Precipitation was negatively correlated at lags 1
and 2, suggesting that reduced recent precipitation is associated with higher food prices. Overall, these results
support the inclusion of all predictors and the Food Price Index at lag 3 for modeling. e inclusion of 3-month
lagged predictors was designed to capture the economic persistence of the Food Price Index, ensuring the model
internalizes the autoregressive properties of the series similar to classical econometric frameworks.
To validate the selection of the temporal lag, a comprehensive sensitivity analysis was performed by testing
lags of 1, 3, 6, 12, and 18 months across multiple neural network architectures (Table 3). While the results indicate
that a 1-month lag may produce low training errors in some instances, this conguration was intentionally
excluded to mitigate the risk of overtting and to ensure the models capture meaningful temporal dependencies
rather than short-term noise. Consequently, the analysis demonstrates that the 3-month lag provides the most
robust predictive precision, specically within the NN [8] and NN [6] architectures, yielding the lower veried
Root Mean Square Error (RMSE) and strong coecient of determination (
R2
). Error rates (RMSE) signicantly
increase as the horizon extends to 6, 12, or 18 months, reaching a peak error of 17.138. ese ndings conrm
that a 3-month lag provides the optimal balance for capturing the delayed impacts of climate shocks and energy
price volatility on food ination in Bangladesh.
e study employed a mixed lag structure: some variables were included at the current time point (t), and
others, including the Food Price Index, were incorporated with a time lag of three months (
t−3
). is approach
serves as a form of feature engineering, creating new features from the existing raw data formats. Most recent
information not only keeps the model simple by avoiding overtting but also enhances computational eciency
by training the model faster than a model with a higher lag. Results from this study demonstrate that a lag of
3 holds sucient predictive power, enabling strong performance without the need for a more complex model.
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
0.00.2 0.40.6 0.81.0
Lag
ACF
Food Price Index
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
−0.15−0.10 −0.050.000.050.100.15
Lag
ACF
Monthly Average Surface Te mperatures (°C) & Food Price Index
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
0.00.2 0.40.6 0.81.0
Lag
ACF
Energy Price Index & Food Price Index
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
−0.1 0.00.1 0.20.3
Lag
ACF
Temperature Anomalies by Month (°C) & Food Price Index
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
−0.2 −0.1 0.00.1
Lag
ACF
Monthly Precipitation & Food Price Index
(a) Cross-correlation function (CCF)
0.0
0.5
1.0
1.5
2015 2020 2025
Time
Normalized Data
series
Food Price Index
Monthly Average
Surface
Temperatures (°C)
Energy Price Index
Temperature
Anomalies
by Month (°C)
Monthly Precipitation
FPI_lag3
MAST_lag3
EPI_lag3
TAM_lag3
MP_lag3
(b) Lagged data at time (t-3)
Fig. 4. Illustration of the normalized time series along with its corresponding lagged features. Subgures (a)
and (b) highlight distinct characteristics of the data from two analytical perspectives: the temporal correlation
structure and the representation of the selected lagged features used in the models.
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Data normalization
ANN is highly sensitive to the scale or range of input data, as extremely scattered or volatile data can dominate
the learning process, leading to slower convergence. at is why it is best practice to scale or normalize the data
of each variable within a range during the preprocessing stage. Using min-max scaling, the study can ensure
that all features contribute proportionally to the network’s learning process and help in stabilizing the training.
x
normalized =
x−x
min
xmax −xmin
(3)
where x is the original value,
xmin
is the minimum value of the feature, and
xmax
is the maximum value of the
feature39.
e data set with the lagged features was scaled within 0 and 1, using the preprocess function of the caret
package with the range method and the normalized data was made ready for modeling (Fig. 4b).
For time series forecasting, the inherent temporal dependencies of the data must be explicitly captured. e
major drawback of a general ANN is that it cannot process the intrinsic temporal dependencies of the time
series data. Regardless of the number of layers or inputs, ANN takes the data of features as each datapoint is
independent of time. Hence, A Time-Delay ANN (oen conceptualized as a NAR(X) network) is ideally suited
for this purpose20. is architecture incorporates past observations of the target variable and potentially other
relevant exogenous variables as inputs to predict future values.
e “Time-Delay” aspect refers to the inclusion of historical data points as features. It is a popular method
of feature engineering, the creation of new features out of existing variables, widely used in machine learning
practice and other scientic research domains.
For instance, to predict the food price index at time t, the model considers prices at
t−1,t−2,...,t−k
,
where k/m represents the number of time lags, allowing the network to learn how past price movements inuence
future ones. e general form of such a model can be represented as:
Yt=f(Yt−1,Y
t−2,...,Y
t−k,E
t−1,E
t−2,...,E
t−m)
(4)
where
Yt
is the food price index at time t,
Yt−i
are past output values,
Et−j
are past values of exogenous
variables, and
f(·)
is the non-linear mapping function learned by the ANN. e mathematical equation can be
rewritten incorporating the selected target output and the exogenous inputs along with their lagged components
for this study.
FPI
t
=f(FPI
t−3
, MAST
t
,EPI
t
, T AM
t
,MP
t
, MAST
t−3
,EPI
t−3
,
T AM
t−3
,MP
t−3)
(5)
Here is a breakdown of the variables used in the equation:
Model Architecture Lag RMSE
R2
ANN [8]
1 7.926 0.859
3 6.836 0.898
6 8.487 0.843
12 12.316 0.901
18 17.138 0.765
ANN [6, 4]
1 12.74 0.867
3 13.268 0.781
6 14.571 0.795
12 15.535 0.874
18 16.647 0.803
ANN [6]
1 3.174 0.931
3 9.812 0.79
6 12.944 0.648
12 15.119 0.868
18 16.468 0.705
ANN [8, 14]
1 10.013 0.882
3 10.483 0.857
6 8.876 0.833
12 11.217 0.935
18 16.502 0.741
Table 3. Sensitivity analysis of input lag lengths on TDANN prediction performance. e table reports RMSE
and
R2
for ANN models with varying hidden-layer structures and input lags.
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•
FPI
t
: Predicted Food Price Index at the current time (t).
•
FPI
t−3
: Food Price Index from three time periods earlier (
t−3
).
•
MASTt
: Monthly Average Surface Temperatures at time t.
•
EPIt
: Energy Price Index at time t.
•
T AMt
: Temperature Anomalies by Month at time t.
•
MPt
: Monthly Precipitation at time t.
•
MASTt−3
: Monthly Average Surface Temperatures from three time periods earlier (
t−3
).
•
EPIt−3
: Energy Price Index from three time periods earlier (
t−3
).
•
T AMt−3
: Temperature Anomalies by Month from three time periods earlier (
t−3
).
•
MPt−3
: Monthly Precipitation from three time periods earlier (
t−3
).
In this equation, f represents the non-linear function computed by the ANN, which takes the set of nine input
variables to predict the output variable,
FPI
t
. is structure enables the model to capture autocorrelation and
other dynamic relationships within the target series.
Activation function
Hidden layers: logistic (sigmoid) activation
Next, the choice of activation function is critical for introducing non-linearity and determining the output
range of neurons. Among the conventional activation functions for ANN, this study employed the sigmoid
function40,41, which can be dened as:
S
(x)=
1
1+e−
x (6)
S(x) represents the output of the sigmoid function, which always falls between 0 and 1. It’s commonly used to map
any real-valued number into a value that can be interpreted as a probability while x is the input variable to the
function. It can be any real number from
−∞
to
+∞
and e is Euler’s number, an irrational and transcendental
number that serves as the base of the natural logarithm. Its approximate value is 2.71828. e output of the
sigmoid function is bounded between 0 and 1. is characteristic is benecial for hidden layers as it helps to
compress the input values into a small, manageable range, preventing the vanishing gradient problem to some
extent in earlier layers and allowing the network to learn complex, non-linear relationships.
Output layer: linear activation
ough the sigmoid function is ne for the hidden layer, it is not appropriate for the output layer. e
prediction values of the output layer will be constrained within bounded scores, like the normalized data, and as
a result, the model might fail to accurately predict the scores, limiting the forecast ability of the model even aer
denormalization. A linear activation function is used for the output layer. A linear activation function simply
passes the weighted sum of inputs directly as the output:
l(x)=x
(7)
Aer combining the inputs with the initial normalized data, the linear output layer produces prediction values in
the 0–1 range, which later can be turned back to its original scale for practical interpretation.
Prophet
Facebook’s core Data Science team developed the Prophet model, a highly intuitive time series analysis model
for forecasting. It is a fruitful model for time series data exhibiting strong seasonal eects (like daily, weekly, or
yearly patterns) and has historical data with missing values or outliers. e model’s customizable nature makes
it convenient for analysts without deep expertise in time series forecasting. A decomposable time series model
forms the footing of the Prophet model, comprising three main components: trend, seasonality, and holidays.
Prophet follows a simple additive regression approach to model these components42.
e trend component measures non-periodic changes in the time series, and Prophet has two types of
trend models: linear and logistic. e trend follows as a piecewise linear or logistic function, capturing abrupt
changes in the growth rate known as changepoints, which can be manually specied. e Prophet model is well
suited to capture the complexity of yearly, monthly, and daily seasonality in food prices, as price uctuations
in Bangladesh are directly linked to crop cycles, harvesting methods, and festivals. Prophet utilizes the Fourier
series to model the seasonality of time series by smoothing the seasonal curve, letting the model grasp complex
seasonal patterns without having to set any functions or hold assumptions.
e holiday component of the model captures the irregularities in time as a separate one-time shock apart
from xed seasonal intervals. e general level of food price is moderately sensitive to holidays in Bangladesh, as
the supply and demand of food items changes according to public consumption. For example, during Eid every
year, the demand for meat and chicken soars higher than at any other time of the year, or the price of sweets gets
higher around Independence Day or Victory Day for celebration. For each holiday in the data, a dummy variable
is devised, which inserts 1 for the holiday and 0 otherwise.
e full model for forecasting the Food Price Index, based on the Prophet framework43,44, can be expressed
as:
FPI
(t)=g(t)+s(t)+h(t)+
n
∑
i=1
βixi(t)+ϵ
t
(8)
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e equation can be rewritten as:
FPI
t
=
g
(
t
)+
s
(
t
)+
h
(
t
)+
β1EPIt
+
β2T AMt
+
β3MPt
+
ϵt (9)
where
•
FPI
t
: e target output, the Food Price Index at time t.
• g(t): e linear trend of the series.
• s(t): e seasonal eects, such as monthly or yearly patterns.
• h(t): e component for the impact of predened holidays or events.
•
β1,β
2,β
3
: e coecients for the external regressors at time t.
•
EPIt, T AMt,MPt
: e external regressor variables included at time t.
•
ϵt
: e error term of the model.
is paper incorporated external regressors for a robust Prophet model in order to conduct a rigorous predictive
analysis of the food price index. e external regressors represent the linear inuence of external events. In
Fig. 2, the Pearson Correlation Matrix conrmed a strong multicollinearity between the lagged values of two
external regressors: monthly average surface temperatures and monthly precipitation (r=0.74). Both variables
were sharing the same predictive power. e one with the lower correlation with FPI (r=0.01) was dropped from
the model to remove redundancy. e MAST at lag 3 did not provide any new information to the Prophet model.
LSTM theoretical framework
e Long Short-Term Memory (LSTM) network, a specialized form of Recurrent Neural Network, serves as a
powerful non-linear alternative to TDANN for modeling complex multivariate time series45. is model can
automatically learn features such as trends and seasonality in time series data without the need for manual
dierencing or seasonal decomposition. To leverage the available variables: the target
FPIt
(Food Price Index)
and the four exogenous variables (
MAST
,
EPI
,
TAM
, and
MP
), the model is congured as an
LSTMX
(LSTM
with Exogenous Regressors). Data preprocessing requires transforming the time series into overlapping
sequences of xed length (the lookback window), resulting in a feature matrix where each input vector
xt
contains all ve variables.
Core LSTM gates and state update
e core LSTM cell dynamically regulates information ow using three gates (
σ
is the sigmoid activation function
and
tanh
is the hyperbolic tangent). e Forget Gate (
ft
) decides what to discard from the previous Cell State
(
Ct−1
), while the Input Gate (
it
) and Candidate Cell Value (
˜
Ct
) decide what new information to store45,46.
ft=σ(Wf·[ht−1,xt]+bf)
(10)
i
t
=σ(W
i
·[h
t
−1,x
t
]+b
i
)
(11)
˜
Ct= tanh(WC·[ht−1,xt]+bC)
(12)
e Cell State (
Ct
), or long-term memory, is then updated:
Ct=ft⊙Ct−1+it⊙˜
Ct
(13)
Finally, the Output Gate (
ot
) determines what information from the cell state is exposed as the Hidden State (
ht
),
which is used for the prediction layer.
ot=σ(Wo·[ht−1,xt]+bo)
(14)
ht=ot⊙tanh(Ct)
(15)
Forecasting the food price index
e LSTM learns a complex non-linear function G that maps the sequence of inputs to the future Food Price
Index
ˆ
FPIt+∆t
:
ˆ
FPI
t+∆t
=
G
(
FPI
t−L,...,FPI
t
Lagged Target
,
x
t−L,...,
x
t+∆t
Multivariate Features
)
(16)
e input vector
xt
at each time step t combines the features:
xt=[FPI
t,MASTt,EPIt,TAM t,MPt]
(17)
By training on these multivariate input sequences, the LSTM learns a complex function that maps the historical
co-evolution of the variables to the future
ˆ
FPIt+∆t
, providing a exible and robust framework for forecasting
under the inuence of both temporal and external factors.
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Evaluation metrics
e performances of all the ANN models and the Prophet are evaluated using multiple statistical techniques:
Root Mean Square Error (RMSE), R-squared (
R2
), and Mean Absolute Error (MAE).
Root Mean Square Error (RMSE)
RMSE is a measure of the average magnitude of the errors between predicted values and actual values. Because
the errors are squared before being averaged, RMSE gives a higher weight to large errors, making it useful when
signicant errors are particularly undesirable. It is expressed in the same units as the dependent variable, which
makes it easy to interpret.
e formula for RMSE is:
RMSE
=
1
n
n
i=1
(yi−ˆyi)
2
(18)
In this formula, n is the number of data points,
yi
is the actual value, and
ˆyi
is the predicted value.
R-squared (
R2
)
R-squared, or the coecient of determination, is a statistical measure that represents the proportion of the
variance in the dependent variable that is predictable from the independent variable(s) in a regression model.
Provides an indication of how well the model ts the observed data, with values ranging from 0 to 1. A higher
value (closer to 1) means that the model predictions more accurately explain the observed data.
e formula for R-squared is:
R
2=1−
∑n
i=1
(
yi−
ˆ
yi
)2
∑
n
i=1(
y
i−¯
y
)
2 (19)
Here,
yi
is the actual value,
ˆyi
is the predicted value,
¯y
is the mean of the actual values, and n is the number of
data points.
Mean Absolute Error (MAE)
MAE measures the average magnitude of the errors in a set of predictions, without considering their direction.
It is the average of the absolute dierences between the predicted and actual values. Unlike RMSE, MAE gives all
errors equal weight, making it less sensitive to outliers. It is oen preferred for its straightforward interpretability
and robustness to extreme values.
e formula for MAE is:
MAE
=
1
n
n
∑
i=1
|yi−ˆyi
|
(20)
In this formula, n is the number of data points,
yi
is the actual value, and
ˆyi
is the predicted value.
Results
SARIMAX
is specic SARIMAX model was built in R using the Arima function, with the orders for both seasonal and
non-seasonal lags automatically determined by the auto.arima function. However, the order of the seasonal MA
was manually set to improve the model as the AIC values were not good determinants of a good t. e author
ultimately selected the nal model’s orders (0, 0, 2) and seasonal orders (0, 0, 3) based on further analysis, such as
ACF/PACF inspection and domain expertise (Fig. 5a), and then used this specic model to generate the forecast
set on the future test data. e selected model is the best alternative among multiple architectures with dierent
parameters.
In Fig. 5b, actual values (Food Price Index) are shown by a solid black line, demonstrating an overall upward
trend over the period shown, peaking near the end of the data. Predicted values are represented by a dashed
blue line, which generally follows the trend of the actual data but with less volatility. A shaded light blue area
surrounding the predicted line represents the condence interval (95%), showing the range of uncertainty for
the SARIMAX forecast. e plot covers a period from April, 2022 to March, 2025. Visually, the SARIMAX model
captures the general direction, but the actual Food Price Index experienced higher peaks and troughs than
predicted, especially in the later part of the test set where the actual line moves outside the shaded condence
band.
e accompanying residual diagnostic plots (shown in 5c) for the ARIMA (0,0,2) (0,0,3) [12] model reveal
the following: e residuals appear to be relatively centered around zero and show no clear pattern or increasing
variance, suggesting the model captures the underlying structure well. However, there are a few signicant spikes
(around 2016 and 2017). e Autocorrelation Function (ACF) plot shows that several signicant spikes remain
outside the dashed blue condence bounds. is indicates that the residuals are autocorrelated, meaning there
is still predictable information (pattern) le in the errors that the model failed to capture. e histogram of the
residuals shows a distribution that is normal (bell-shaped curve), which is a favorable characteristic. While the
model follows the general trend and the residuals are normally distributed, the signicant autocorrelation in the
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residuals (ACF plot) suggests that the chosen SARIMAX (0,0,2) (0,0,3) [12] may not be the optimal t and could
be improved by adjusting the model orders to account for the remaining structure in the errors.
e residual patterns are complex or do change over time; this calls for the necessity of trying dierent model
ts to capture the full dynamics of FPI, and a non-linear approach might be suitable for capturing the complex
relationships of FPI including external variables.
Modeling the neural networks
e study eectively prevented data leakage through methodical application of two time-series-specic
preprocessing techniques: Chronological Splitting and Training-Set-Based Normalization. First, the study
generated the nal feature set, where predictors were based on the past 3-month lagged values. e study then
divided this feature set into training (80%) and testing (20%) subsets strictly based on time sequence. e training
data contained observations that occurred entirely before the observations in the test data. is technique
prevented look-ahead bias by ensuring the model’s training only utilized historical information relative to the
forecast period. e study t the Min-Max scaler (a transformation process) only on the training data. is
involved calculating the minimum and maximum values for each feature solely from the training set. ese
scaling parameters were then applied consistently to both the training set and the future test set. is prevented
test-set contamination, as the scaling of the training data was not inuenced by the statistical properties (like
the future range) of the test data. By adhering to these steps, the study respected the temporal dependency of the
data, ensuring the subsequent model was built on a foundation that accurately simulated real-world forecasting.
A grid search was conducted to nd the optimal hyperparameters for the expected neural network (NN)
model using expanding window cross-validation (CV). Forty hyperparameter combinations were systematically
iterated through R codes. For each combination, R trained and evaluated the TDANN model across ve
expanding data folds (where the training set grows over time), calculating the Root Mean Squared Error (RMSE)
for each fold. Finally, the RMSE across the folds was averaged to assess the model’s performance, and a range of
condence intervals for the mean RMSE of each combination was calculated (Table 4).
0.00.5 1.01.5
0.00.2 0.40.6 0.81.0
Lag
ACF
ACF − Food Price Index
0.51.0 1.5
0.00.2 0.40.6 0.8 1.0
Lag
Partial ACF
PACF − Food Price Index
(a
)ACF andPACFplotsfor theFood
Price
Index. Theslowdecay in theACF
an
dthe single dominant PACF spikeat
la
g1indicate ahighlypersistentnon-
stationary
time series.
100
110
120
130
140
2023 202
42
025
Date
Food Price Index
Actual
Predicted
SARIMAX Forecast vs Actual (Test Set)
(b)SARIMAX TimeSeries Forecast:
PointEstimates and 95% ConfidenceI
n-
terval(BlueShadedRegion)
−4
−2
0
2
2010 2012 2014 2016 2018 2020 2022
Residuals from Regression with ARIMA(0,0,2)(0,0,3)[12] errors
0.0
0.2
0.4
12 24 36
Lag
ACF
0
10
20
−4 −2 02
residuals
df$y
(c) ResidualAnalysisofthe SARIMAX
Model
Fig. 5. Visualization of SARIMAX model performance: (a) ACF and PACF Plots, (b) Time series forecast with
condence intervals and (c) corresponding residual analysis.
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e author adhered to applying the parsimony principle by selecting a simpler or more stable model if its
performance is statistically equivalent to the one with the lowest error. e study made a trade-o between
model performance and model complexity/stability for better forecasting accuracy. e selection criteria for the
nal modeling were not just based on the minimum average RMSE but also on a more robust, statistically backed
approach to prevent overtting/undertting and improve real-world forecasting accuracy.
Aer having the normalized data in training and testing, 80% and 20%, respectively, the study initiated
conguring the hyperparameters of the neural networks utilizing R’s neuralnet package37. Four NN architectures
are built with distinct key congurations, and each of the neural networks is run through ve repetitions, keeping
the same activation functions (sigmoid and linear) for both the hidden and the output layers, with the intention
of nding the most accurate models with the lowest possible error (Table 5). e formula (‘Food.Price.
Index’
˜
.) tells R to model the Food Price Index as a linear function of all the other external and lagged variables
present in the dataset. e threshold parameter of the neuralnet function species the stopping criterion of the
training algorithm, implying that further training beyond this point would not bring about much improvement.
e value 0.01 was set as an adjusted threshold to stop training when the partial derivative of the error function
No. Hidden reps reshold mean_rmse rmse_se rmse_ci_lower rmse_ci_upper
1 8 1 0.01 0.063586065 0.010897964 0.033328466 0.093843664
2 8 1 0.005 0.052665573 0.016874642 0.005814055 0.099517092
3 8 2 0.01 0.054856753 0.011888721 0.021848371 0.087865136
4 8 2 0.005 0.057261625 0.013758332 0.019062371 0.095460879
5 8 3 0.01 0.054983566 0.006865484 0.035921926 0.074045206
6 8 3 0.005 0.053944617 0.009277045 0.028187412 0.079701822
7 8 4 0.01 0.064519442 0.020813013 0.006733252 0.122305631
8 8 4 0.005 0.054795181 0.014327681 0.015015161 0.094575202
9 8 5 0.01 0.082418083 0.027851112 0.005090999 0.159745167
10 8 5 0.005 0.057349187 0.010482752 0.028244403 0.086453972
11 6-4 1 0.01 0.085426727 0.014707985 0.044590814 0.126262639
12 6-4 1 0.005 0.053561311 0.008087784 0.031106022 0.076016599
13 6-4 2 0.01 0.096507021 0.014450267 0.056386647 0.136627396
14 6-4 2 0.005 0.073042493 0.015586034 0.029768724 0.116316262
15 6-4 3 0.01 0.107630113 0.021347498 0.048359955 0.16690027
16 6-4 3 0.005 0.080392952 0.019037717 0.027535777 0.133250128
17 6-4 4 0.01 0.08912159 0.017893393 0.039441565 0.138801614
18 6-4 4 0.005 0.067885213 0.015901127 0.023736606 0.112033819
19 6-4 5 0.01 0.088913008 0.011883063 0.055920337 0.121905679
20 6-4 5 0.005 0.073978235 0.012848192 0.038305935 0.109650534
21 6 1 0.01 0.069688104 0.020394993 0.013062524 0.126313684
22 6 1 0.005 0.058277452 0.006602074 0.039947155 0.076607749
23 6 2 0.01 0.067360303 0.01104982 0.036681084 0.098039522
24 6 2 0.005 0.058526601 0.013200018 0.021877477 0.095175726
25 6 3 0.01 0.04279231 0.004480262 0.03035311 0.05523151
26 6 3 0.005 0.070511423 0.012711504 0.035218631 0.105804216
27 6 4 0.01 0.077906692 0.02255615 0.01528078 0.140532604
28 6 4 0.005 0.063112151 0.020082005 0.007355567 0.118868734
29 6 5 0.01 0.078418422 0.018955286 0.025790111 0.131046734
30 6 5 0.005 0.064647839 0.015425654 0.021819356 0.107476321
31 8–14 1 0.01 0.079391624 0.010579307 0.050018759 0.108764489
32 8–14 1 0.005 0.066454149 0.021190416 0.007620122 0.125288176
33 8–14 2 0.01 0.064568016 0.008751163 0.040270893 0.08886514
34 8–14 2 0.005 0.0624409 0.016550424 0.016489557 0.108392243
35 8–14 3 0.01 0.091999914 0.013576538 0.0543054 0.129694428
36 8–14 3 0.005 0.051529299 0.005889331 0.035177894 0.067880704
37 8–14 4 0.01 0.077889417 0.006829141 0.058928681 0.096850153
38 8–14 4 0.005 0.089123201 0.023111861 0.024954387 0.153292015
39 8–14 5 0.01 0.070956607 0.010986623 0.04045285 0.101460364
40 8–14 5 0.005 0.075660005 0.013898127 0.037072619 0.114247391
Table 4. Results of 40 Combinations of Hyperparameters from Grid Search with Expanding Window Cross-
Validation.
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with respect to the weights falls below this point. e lower the threshold, the better the accuracy with more
training time. e Lifesign parameter is for monitoring the overall progress to inspect whether the models
are converging or having a decreasing error rate. Each of the NNs was designed with dierent combinations
of hidden layers and nodes aer iterating through exhaustive hyperparameter tuning or optimization. Finally,
the selected architectures: NN [8], NN [6, 4], NN [6], and NN [8, 14], are taken further to t the training data.
Simultaneously, the study has only taken the particular repetition out of 5, revealing lower error with the best t
for each model, and these models are employed to predict the values on the test data. Selected neural network
architectures are portrayed in Figs. 6,7,8,9 with the customizable ggplot function of the ggplot2 package in R, an
elegant and powerful visualization tool47.
A central tendency of the weight distribution in a neural network is desirable, as it promotes symmetry
breaking, prevents vanishing gradients, and is a sign of regularization. A weight distribution centered around
zero implies that each neuron starts with a unique set of weights, allowing neurons to learn dierent features
without giving one feature more signicance over the other. is is crucial for unbiased inuences of features on
the output. Initializing weights with a central tendency of zero and a small variance keeps the gradients within
a stable range, ensuring that the network can learn eectively. Meanwhile, central tendency also regularizes to
restrain large weights to prevent the model from overtting. e density curves in Fig. 10 demonstrate that the
four models have weights centered around zero, insinuating that the proper regularization methods work as
intended, leading to a more generalized model that performs well on unseen data. It also serves as a stabilizing
mechanism during regime transitions. By preventing explosive gradients, this constraint ensures that the model
identies stable underlying signals rather than overtting to transient volatility or structural shocks.
For the convenient analysis of the Food Price Index, the nal models were designated as follows: ANN [8]
(from NN [8] at rep = 2), ANN [6, 4] (from NN [6, 4] at rep = 1), ANN [6] (from NN [6] at rep = 1), and ANN [8,
14] (from NN [8, 14] at rep = 4). In the visual representations of the performances of each model on the observed
data, it is seen that out of the four neural networks, ANN [6] is projecting the predictions closest to the unseen
test series (Figs. 11,12,13,14,15).
Feature importance
Inspired by the cooperative game theory concept, SHAP (SHapley Additive exPlanations) is a powerful and
widely utilized method to explain the intricate predictions of machine learning models based on Shapley
I1
I2
I3
I4
I5
I6
I7
I8
I9
Monthly Average
Surface
Temperatures (°C)
Energy Price Index
Temperature
Anomalies
by Month (°C)
Monthly Precipitation
FPI_lag3
MAST_lag3
EPI_lag3
TAM_lag3
MP_lag3
H1
H2
H3
H4
H5
H6
H7
H8
O1 Food Price Index
B1 B2
Neural Network [8]
error: 0.0263 | steps: 741 | rep: 2
Fig. 6. Neural network architecture with 8 nodes in the hidden layer.
No. Model
Nodes Activation
Function
Adjusted reshold Lifesign Rep CovariateHidden Layer 1 Hidden Layer 2 Hidden Output
1 TDANN 8 Sigmoid Linear 0.01 Minimal 5 9
2 TDANN 6 4
3 TDANN 6
4 TDANN 8 14
Table 5. Neural network hyperparameter optimization.
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values48. e core idea is grasped from game theory to understand the contributions of each feature in predicting
the output in a model. In this study, features (e.g., Energy Price Index, Monthly Precipitation) are the players
of the normalized dataset. For each specic datapoint, the ANN’s prediction is the game, and the payout is the
dierence between the model’s prediction and the average prediction across the entire dataset (or a specied
baseline). To enunciate it more elaborately, SHAP values are calculated by determining the dierence between
the predicted values with and without the addition of each feature for all combinations, and taking the average.
us, it becomes feasible to understand which feature has contributed to what extent or how much in inuencing
output (prediction) signicantly, regardless of whether the inuence is positive or negative49,50.
Articial Neural Networks are oen referred to as ”black-box” models due to their architectural mystery:
non-linear nature, and weight distribution process, making their predictions problematic to interpret. Trust
in black-box model predictions can be built by the explainability provided through SHAP51. SHAP helps to
demystify the underlying operations of models by showcasing local and global Interpretability. Every prediction
by the model can be explained by the SHAP, which indicates how much each feature contributed to pushing the
model’s output from the average baseline to the nal predicted value. Simultaneously, by aggregating the SHAP
values across the entire dataset of predictions, the holistic picture of the feature importance is obtained.
I1
I2
I3
I4
I5
I6
I7
I8
I9
Monthly Average
Surface
Temperatures (°C)
Energy Price Index
Temperature
Anomalies
by Month (°C)
Monthly Precipitation
FPI_lag3
MAST_lag3
EPI_lag3
TAM_lag3
MP_lag3
H1
H2
H3
H4
H5
H6
O1 Food.Price.Index
B1 B2
Neural Network [6]
error: 0.0201 | steps: 879 | rep: 1
Fig. 8. Neural network architecture with 6 nodes in the hidden layer.
I1
I2
I3
I4
I5
I6
I7
I8
I9
Monthly Average
Surface
Temperatures (°C)
Energy Price Index
Temperature
Anomalies
by Month (°C)
Monthly Precipitation
FPI_lag3
MAST_lag3
EPI_lag3
TAM_lag3
MP_lag3
H1
H2
H3
H4
H5
H6
H1
H2
H3
H4
O1 Food.Price.Index
B1 B2 B3
Neural Network [6, 4]
error: 0.0297 | steps: 258 | rep: 1
Fig. 7. Neural network architecture with 6 nodes in the rst hidden layer and 4 nodes in the second hidden
layer.
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e author has employed the DALEX (moDel Agnostic Language for Exploration and eXplanation) package,
based on Kernel SHAP algorithm, which is designed to be a central toolkit for explaining the behavior of any
predictive model, regardless of its underlying algorithm52. DALEX::explain created a model wrapper, which
is then passed to predict_parts(type = ”shap”) to compute SHAP values for the features. e study
proceeded with the NN [6] as its rst repetition generated the best predictions at the lowest error, and calculated
SHAP values for test data observations.
A SHAP summary plot (Fig. 16) is created to reveal the individual impact of each feature, colored in
accordance with its scaled value and ranked in order of importance, demonstrating the overall behavior of
0.0
0.1
0.2
0.3
0.4
−20 −10 01
02
0
Weight Value
Density
Model NN [6, 4], rep=1 NN [6], rep=1 NN [8, 14], rep=4 NN [8], rep=2
Weight Distribution of TDANN Models
Fig. 10. Density plot manifesting the distribution of trained weights for various neural network models. is
visualization provides insight into how architecture choices inuence weight value ranges, which is a critical
factor in model regularization.
I1
I2
I3
I4
I5
I6
I7
I8
I9
Monthly Average
Surface
Temperatures (°C)
Energy Price Index
Temperature
Anomalies
by Month (°C)
Monthly Precipitation
FPI_lag3
MAST_lag3
EPI_lag3
TAM_lag3
MP_lag3
H1
H2
H3
H4
H5
H6
H7
H8
H1
H2
H3
H4
H5
H6
H7
H8
H9
H10
H11
H12
H13
H14
O1 Food.Price.Index
B1 B2 B3
Neural Network [8, 14]
error: 0.0299 | steps: 330 | rep: 4
Fig. 9. Neural network architecture with 8 nodes in the rst hidden layer and 14 nodes in the second hidden
layer.
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the articial neural network model. e Global Feature Importance is represented with the bar plot (Fig. 17)
depicting the mean absolute SHAP value for each input in the test set. From both of these essential gures, it is
crystal clear that the Food Price Index at lag 3, the Monthly Precipitation at lag 3, and Energy Price Index are
the greatest contributors with higher scores in predicting the Food Price Index, whereas Monthly Precipitation,
0.0
0.5
1.0
1.5
2010−11 2011−09 2012−07 2013−05 2014−03 2015−01 2015−11 2016−09 2017−07 2018−05 2019−032020−01 2020−11 2021−09 2022−07 2023−05 2024−03 2025−01 2025−11
Time
Food Price Index
Legend
Actual
ANN − Fitted
ANN − Predicted
ANN [6, 4] vs Observed
Fig. 12. e t and predictive performance of the ANN [6, 4] with the normalized Food Price Index data,
illustrating the model’s accuracy on unseen future price trends.
0.0
0.5
1.0
1.5
2010−11 2011−09 2012−07 2013−05 2014−03 2015−01 2015−11 2016−09 2017−07 2018−05 2019−032020−01 2020−11 2021−09 2022−07 2023−05 2024−03 2025−01 2025−11
Time
Food Price Index
Legend
Actual
ANN − Fitted
ANN − Predicted
ANN [8] vs Observed
Fig. 11. e t and predictive performance of the ANN [8] with the normalized Food Price Index data,
illustrating the model’s accuracy on unseen future price trends.
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Monthly Average Surface Temperatures at lag 3, and Monthly Average Surface Temperatures are moderately
strong contributors. Temperature Anomalies by Month is almost insignicant but relevant (Table 6).
From both the SHAP Summary and the Global Feature Importance plots, it is evident that the Food Price
Index at lag 3 is the most inuential feature, and the Monthly Precipitation at Lag 3 is the second most inuential
feature in contributing to the prediction of the Food Price Index.
0.0
0.5
1.0
1.5
2010−11 2011−09 2012−07 2013−05 2014−03 2015−01 2015−11 2016−09 2017−07 2018−05 2019−03 2020−012020−11 2021−092022−07 2023−05 2024−032025−01 2025−11
Time
Food Price Index
Legend
Actual
ANN − Fitted
ANN − Predicte
d
ANN [8, 14] vs Observed
Fig. 14. e t and predictive performance of the ANN [8, 14] with the normalized Food Price Index data,
illustrating the model’s accuracy on unseen future price trends.
0.0
0.5
1.0
1.5
2010−11 2011−09 2012−07 2013−05 2014−03 2015−01 2015−11 2016−09 2017−07 2018−05 2019−03 2020−012020−11 2021−092022−07 2023−05 2024−032025−01 2025−11
Time
Food Price Index
Legend
Actual
ANN − Fitted
ANN − Predicte
d
ANN [6] vs Observed
Fig. 13. e t and predictive performance of the ANN [6] with the normalized Food Price Index data,
illustrating the model’s accuracy on unseen future price trends.
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e GFI (Mean Absolute SHAP Value) shows the global view of feature strength regardless of direction. It
does not tell whether the Energy Price Index makes food prices go up or down. It just tells us that energy prices
move the needle a lot. e SHAP summary plot, in beeswarm style (Fig. 16), is the gold standard for model
interpretation since it combines the local details (the relationship and direction) with a global view on a single
chart. e FPI_lag3, as the strongest feature, pushes the food price prediction up (higher ination) where the
SHAP value is greater than 0, and vice versa. So, here the relationship is positive. On the contrary, MP_lag3 has a
wide spread, which indicates why it is the second strongest, but the colors are mixed, with purple and yellow dots
Temperature Anomalies by Month [°C]
EPI_lag3
TAM_lag3
Monthly Precipitation
MAST_lag3
Monthly Average Surface Temperatures [°C]
Energy Price Index
MP_lag3
FPI_lag3
−0.20.0 0.2
SHAP Value (Impact on Model Output)
Feature
Scaled Feature V
alue
0.0
0.5
1.0
1.5
Impact on model output, colored by feature value
SHAP Summary Plot
Fig. 16. SHAP summary plot ranks features by importance, showing their contribution to the model’s
predictions. e magnitude and color of the SHAP values indicate the strength and direction of a feature’s
impact.
0.0
0.5
1.0
1.5
2010−11 2011−09 2012−07 2013−05 2014−03 2015−01 2015−11 2016−09 2017−07 2018−05 2019−03 2020−01 2020−11 2021−09 2022−07 2023−05 2024−03 2025−01 2025−11
Time
Food Price Index
Legend
ANN [6,4]
ANN [6]
ANN [8,l4]
ANN [8]
FPI
Comparison of four artificial neural network models against observed data
Fig. 15. e plot presents a comparative analysis of the TDANN models, showing that model ANN [6]
achieved the highest accuracy, outperforming all other models.
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overlapping in the middle and sides. e relationship is nonlinear or complex. It’s not as simple as “More rain =
Lower prices.” It might depend on when rain happens or how precipitation mediates other variables.
e study delved deep into understanding the complex relationship between the strongest features of the
TDANN. e study analyzes the SHAP Dependence Chart and SHAP Interaction plots and how they interact
with each other in the pragmatic forecasting of food ination.
e dashed line in Fig. 18a, which is increasing at diminishing returns, in the dependence plot shows the
average marginal eect of the FPI_lag3 value on the Food Price Index prediction. e dependence plot conrms
the price autocorrelation of the Food Price Index; the high FPI_lag3 strongly pushes the price up, while the low
FPI_lag3 pulls the prices down. Here, prior monthly precipitation is only signicant as a modier for prior food
prices. e eect of MP_lag3 has always been consistent in modifying the increasing prior price impact on future
prices, but it does so negligibly.
It testies in favor of the prior prices’ overwhelmingly dominant eect on the future price, which is obvious
since food ination does not change erratically. Low FPI_lag3 (near 1.0) values result in a strong negative
contribution of SHAP (down to −0.2), meaning a low prior FPI pulls the current prediction down. High FPI_
Rank Attribute Mean Absolute SHAP Importance (Mean
Absolute SHAP) General Marginal Sign Nature of Inuence
1 FPI lag3 0.106 Highest Strongly Positive (+) Non-Linear (Increasing
at Diminishing Returns)
2 MP lag3 0.043 High Negative (-) Non-Linear (U-shaped
Avg. Eect)
3 Energy Price Index 0.0401 High Positive (+) Non-Linear (Ination
Amplier)
4Monthly Average Surface
Temperatures [
◦
C] 0.0232 Medium Weakly Negative (-) Non-Linear
5 MAST_lag3 0.016 Medium Weakly Negative (-) Non-Linear
6Monthly Precipitation 0.0111 Medium Negative (-) Non-Linear
7 TAM_lag3 0.0108 Medium Weakly Negative (-) Non-Linear
8 EPI_lag3 0.0107 Low Positive (+) Non-Linear
9Temperature Anomalies by Month
[
◦
C] 0.00358 Lowest Weakly Negative (-) Non-Linear
Table 6. Global feature importance with marginal impact.
Temperature Anomalies by Month [°C]
EPI_lag3
TAM_lag3
Monthly Precipitation
MAST_lag3
Monthly Average Surface Temperatures [°C]
Energy Price Index
MP_lag3
FPI_lag3
0.000 0.025 0.050 0.075 0.100
Mean Absolute SHAP Value
Feature
Based on 35 test observations
Global Feature Importance (Mean Absolute SHAP Value)
Fig. 17. e plot ranks features by their global importance based on their absolute SHAP values, showing how
each feature contributes to the model’s predictions where a higher value indicates a stronger impact.
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lag3 (near 1.7) values result in a strong positive contribution (up to +0.25), meaning a high prior FPI pushes the
current prediction up.
In the graph, there are some irregular gaps between the eects of prior monthly precipitation, mostly colored
in black and purple. But at a higher prior FPI (aer 1.6), some of the eects of MP_lag3 are in orange/yellow,
indicating that at very high prior FPI, the prior precipitation is functioning actively beyond just as a modier.
is intriguing point leads the study to an interaction plot to understand prior precipitation with more
scrutiny (Fig. 18b). e average marginal eect of MP_lag3 is represented by a U-shaped dashed line. During
expected weather patterns under normal conditions, when the feature value of MP_lag3 is between 0.2 and
0.4, it allows the prior FPI to have its persistence (autocorrelation) dominate without interference. But during
extreme weather shocks, when the feature value of the prior MP is very low or very high (below 0.2 or above 0.4),
it introduces volatility and uncertainty into the food supply. Blessed with 1,294 rivers, according to the Ministry
of Water Resources, Bangladesh is an agriculturally rich economy. Severe oods or rain can hamper the regular
supply of agricultural production and destroy valuable harvests. On the contrary, harsh droughts can also stall
the normal growth of crops, rice, and vegetables. In mid-year, having a natural state of humidity is crucial, as
April-July is the peak season for rice harvesting. A signicant lack of water can severely impact the plant at nearly
every stage of its life cycle, leading to massive yield reductions.
Such an eect creates challenging circumstances for policymakers to quantify the uncertainty of weather
shocks and damage control. ese two extreme weather shocks break the regular pattern of the current FPI.
e model learns that when the weather is extreme, the FPI history may be a less stable predictor, but in specic
−0.2
−0.1
0.0
0.1
0.2
1.01.2 1.41.6
Feature Value (FPI_lag3)
SHAP Value (Contribution to FPI Prediction)
MP_lag3 Value
0.2
0.4
0.6
0.8
Contribution of FPI_lag3, conditioned by MP_lag3
SHAP Dependence Chart for FPI_lag3
(a)SHAPDependenceChart
−0.2
−0.1
0.0
0.1
0.2
0.00.2 0.40.6 0.8
Feature Value (MP_lag3)
SHAP Value for FPI_lag3
FPI_lag3 Value
1.0
1.2
1.4
1.6
How MP_lag3's value influences FPI_lag3's contribution
Interaction: FPI_lag3 SHAP Value vs. MP_lag3 Value
(b) Interaction Plot 1
−0.2
−0.1
0.0
0.1
0.2
1.01.2 1.41.6
Feature Value (Energy Price Index)
SHAP Value for FPI_lag3
FPI_lag3 Value
1.0
1.2
1.4
1.6
How Energy Price Index's value influences FPI_lag3's contribution
Interaction: FPI_lag3 SHAP Value vs. Energy Price Index Value
(c) InteractionPlot 2
Fig. 18. Overall visualization of SHAP analysis, featuring (a) Dependence Chart positioned above (b) and (c)
two dierent Interaction Plots.
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regimes (high MP_lag3), that extreme weather starts to contribute a larger positive inuence, potentially
signaling upcoming supply issues that drive prices up.
In Fig. 18c, the second interaction plot reveals that the predictive importance of the past FPI value (FPI_lag3)
is not constant; it is strongly conditional on the current Energy Price Index. As the feature value of the energy
price index increases (moving from 1.0 to 1.7), the SHAP value for FPI_lag3 generally increases (moving from
−0.2 to 0.2). e relationship is clearly non-linear and exponential. e positive impact accelerates signicantly
when the Energy Price Index is above 1.4. In simpler terms, FPI_lag3 contributes positively to the prediction
when the Energy Price Index is simultaneously high. If the Energy Price Index is high but FPI_lag3 is low (blue
points in the right cluster), the positive impact is dampened. e policy implication is that policymakers must
focus on keeping current energy costs low to eectively combat future food ination. e model shows that high
past food prices only become a severe inationary problem if current energy costs are also high, meaning energy
acts as an ination amplier. If energy costs are low, they act as a price damper, giving businesses less reason to
raise prices beyond their operational needs, thus osetting the memory of high historical food costs. If the costs
to run farms, maintain arable lands, and acquire agricultural inputs (gas, coal, fuel), factories, and trucks are low,
businesses can’t justify passing on previous high food prices. Low energy acts as a damper on ination.
Modern agriculture is heavily mechanized, meaning energy prices dictate marginal costs of production for
farmers and distributors. High diesel prices increase the cost of running tractors, mixing harvesters, machinery,
and irrigation pumps. Some specic food groups require fuel for instant trucking/shipping and electricity for cold
storage or refrigeration, for instance, shrimp. High energy prices at the macro level directly cause the operational
costs of rms to be high at the micro level. On the other hand, the indirect cost is of equal signicance. High
energy prices hit the farmers twice. e production of nitrogen-based fertilizers is extremely energy-intensive.
When energy prices rise, fertilizer prices almost invariably follow. As a result, the baseline (break-even) price for
crops rises before they are even planted. High fuel and fertilizer costs squeeze margins to zero or negative, but
low fuel and fertilizer costs create a prot margin buer.
While the TDANN is stationarity-agnostic, the SHAP analysis conrms that the model’s internal logic respects
economic fundamentals. e dominance of lagged FPI values highlights the model’s capture of persistence,
while the non-linear interaction eects reect the model’s ability to navigate shiing economic regimes without
the need for manual structural break adjustments.
Forecasting with prophet
In contrast, the Prophet model is built with the prophet function of the prophet package in R53. is function
requires that the data be in a dataframe format with two specic columns: one for the time or date and another
for the target time series variable. e time object in the dataframe is transformed into the Date class. Similar to
neural networks, the same split into a training set and a test set is used to construct the model and validate its
prediction accuracy for consistency. A crucial step before modeling is to relabel the date column as ds and the
Food Price Index as y because the built-in Prophet algorithm only recognizes the time/date variable as ds and
the target variable as y.
e model’s form was xed by choosing linear growth and explicitly including yearly and monthly
seasonality. e parameter tuning focused on prior scales: the seasonality prior scale and changepoint prior
scale were both maintained at the default value of 1, indicating a moderate, neutral allowance for the data to
dene the strength of seasonality and the exibility of the overall trend. Conversely, the regressor prior scale
was strategically increased to 2, signifying a strong weight in the predictive power of the external regressors
(energy, temperature, and precipitation). is highly specied model was ultimately selected because it oered
the best quantitative performance (lowest RMSE) on the holdout test data, leading to the necessary rejection of
alternative specications, such as the model t on scaled data, which yielded inferior results. Manually setting
the changepoint prior scale and seasonality prior scale helps control the exibility of the trend and adjust the
strength of the seasonality, allowing the model to t larger seasonal uctuations smoothly. For the holiday
argument, a custom holiday dataset was extracted from Python’s holidays library54, since R does not have holiday
data for Bangladesh. e yearly seasonality argument was set to TRUE to explicitly tell the model to account for
recurring monthly and yearly patterns. en, external regressors are added using their exact column names in
the Prophet conguration to account for the external inuences on the food price index. Table 7 shows model
parameters used for tuning to improve the predictive performance. Aer tting the model with training data, the
Prophet model is used to predict the values of the Food Price Index on unseen data over a time frame spanning
April 2022 to March 2025 (Fig. 19).
e prophet_plot_components function visualized the decomposed components of the Food Price Index time
series (Fig. 20). e Food Price Index time series shows an upward trend between April 2022 and March 2025,
growing moderately in a linear direction. e day of the year curve shows that the Food Price Index time series
reached its lowest point between April and June and then gradually rose to a higher peak between July and
October. e spikes in the holiday curve at one-year intervals identied recurring events that cause a predictable
and signicant change in the data. Hence, the model has successfully quantied the positive impact of annual
holidays in predicting FPI, a critical part of a well-performing Prophet model. Also, the model has captured the
eects of the additive extra regressors provided, improving prediction accuracy by stabilizing the impact on the
time series, regardless of the trend’s magnitude.
e upward trend of the Prophet forecasts aligns well with the economic reality of Bangladesh, capturing the
observed trend of the Food Price Index. Major structural drivers contribute to this steady rise in food ination.
e positive spikes in the holiday component are dominated by major festivals such as Eid ul-Fitr (End of
Ramadan) and Eid ul-Azha (Festival of Sacrice). Major premium goods such as beef, chicken, milk, sugar,
and vermicelli (for shemai) may experience a massive surge in price due to the heightened demand during and
before both of these festivals. Specically, Eid-ul-Adha creates massive demand and price spikes for livestock
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(cattle, goats, and oxen). High consumer demand, coupled with temporary supply chain disruptions as many
workers and professionals return home for the holidays, creates inationary bottlenecks for the festive foods. e
yearly seasonality component represents the uctuations in prices resulting from agricultural cycles and climate
conditions during the summer and rainy seasons. April to June is the peak harvesting season of the year for major
staple crops: rice Boro, lentils, wheat, and mazie55. e prices fall to their lowest (seasonality score below −50)
because fresh supply saturates the market, easing market pressure by meeting consumer demand suciently.
On the contrary, heavy rainfall and monsoon ooding (typically June to August) disrupt vegetable production
(including onion and potato) and transportation, leading to a shortage and price hike, which explains why the
curve rises aer June.
e extra regressors’ additive component conveys the key ndings about the non-seasonal aspects of the
energy prices, precipitation, and temperature anomalies data in the model. e external shocks represented
by the upward slope from these combined factors suggest that cost-push ination is a major driver of the FPI
forecast. Bangladesh, being a major importer of energy resources, has recently experienced the highly volatile
global prices of oil and fuel that are pressuring the rising expense of domestic production and transportation
costs for food, contributing to the FPI directly. e weather variables (temperature anomalies by month and
60
80
100
120
2010 2015202
02
025
ds
y
Prophet Forecast with External Regressors (Test Set)
Fig. 19. Prophet forecast in blue with the upper and lower
ˆy
values over time (ds). e black points are
observed data and the transparent blue area around the prediction line on the plot represents the 80%
condence interval.
Parameter Value
Growth Type linear
Yearly Seasonality TRUE
Monthly Seasonality TRUE
Weekly Seasonality auto
Daily Seasonality auto
Changepoints 25
Changepoint Prior Scale 1
Seasonality Prior Scale 1
Seasonality Mode additive
Holidays Prior Scale 1
Extra Regressors 3
Regressor Prior Scale 2
Table 7. Prophet parameter conguration.
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monthly precipitation) are proxies for climate risks and supply shocks. Abnormally dry seasons can hurt the
Boro and Aman production, while excessive rainfall or oods can severely damage the expected arable land,
leading to the destruction of crops. It can occur in the short term, but a massive surge in FPI spikes for the
specic groups. e ndings of extra regressors align with the insights of SHAP interaction analysis in the
feature importance section of TDANN. A visualization displays the ANN [6] model’s performance (Fig. 21a)
alongside a direct accuracy comparison between the ANN [6] and Prophet models against the denormalized
Food Price Index (Fig. 21b).
Implementation details of the LSTM
Building on robust time-series methodology, the study eectively handled data processing for the LSTM model
by strictly adhering to two preprocessing techniques. First, the feature set, structured with a sequence length
of 3 time steps (corresponding to 3-month lagged values), was subjected to Chronological Splitting, using a
train ratio of 0.8 (80% training, 20% test). is ensured all training observations occurred temporally before
all test observations, thus preventing look-ahead bias critical for accurate forecasting simulation. Subsequently,
for scaling, the MinMaxScaler with a feature range of (0, 1) was initialized and tted exclusively to the training
data in Python, which calculated the scaling parameters based only on the historical data’s range. ese same
parameters were then consistently used to transform both the training and test sets, eectively preventing test-
set contamination. e resulting scaled features were used to train an LSTM network for 50 Epochs with a Batch
Size of 32, predicting Food Price Index (Table 8). e optimized hyperparameters were determined through
manual tuning. Finally, all Prediction results were inverted using inverse transform to return the forecasts to
their original units.
e learning curve shows that the model stabilizes aer 10 epochs and achieves successful optimization (Fig.
22).
While the Long Short-Term Memory (LSTM) model successfully captures the general upward trend of food
prices over the 33-month period, it exhibits a consistent negative bias, underestimating the peak values observed
in the actual data (blue). Actual prices frequently hover near the upper boundary of the
95%
condence interval
in Fig. 23. e behavior of LSTM’s prediction is similar to that of the SARIMAX.
For activation functions, the standard Keras LSTM defaults were utilized: the sigmoid activation governed
the recurrent gates, while the hyperbolic tangent (tanh) was used for cell state updates, which are crucial for
preventing the vanishing gradient problem. e nal output layer for the regression task used a linear activation.
All training runs employed the Adam optimizer with its ecient, adaptive learning rate mechanism, using the
default Keras settings. Most importantly, the research involved extensive hyperparameter tuning far beyond a
single conguration. is tuning systematically evaluated dierent combinations of units (8, 16, 48, 64, 120, etc.)
and tested a broad spectrum of epochs (ranging from 30 to 500). en the study compared performance using
both 32 and 64 batch sizes. e reported model represents the conguration that achieved the best performance
metrics as determined by this thorough tuning process.
90
100
110
120
2023 2024 2025
ds
trend
0
20
40
60
2023 2024 2025
ds
holidays
−50
−25
0
January 01 April 01 July 01 October 01 January 01
Day of year
yearly
1.5
2.0
2.5
2023 2024 2025
ds
extra_regressors_additive
Fig. 20. e decomposed components of Food Price Index time series: the trend, the holidays, the yearly, and
the extra_regressors_additive.
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e nal Long Short-Term Memory (LSTM) network employed a streamlined stacked architecture with
two recurrent layers of 64 and 32 units, respectively, achieving the lowest overall error metrics among all tested
congurations. is parsimonious structure, derived from a robust hyperparameter tuning process, proved
superior to more complex models (those with higher neuron counts), which were consistently undertting on the
test set. e model utilized a lookback window of 3 months and a minor dropout rate of 0.01 for regularization,
while recurrent dropout was set to zero. e network was trained for 50 epochs using the Adam optimizer (with
default Keras parameters) with a batch size of 32. Notably, attempts to use higher epoch counts, more aggressive
learning rates, or larger batch sizes similarly failed to produce a more stable or better-performing model. It
conrms the optimality of the nalized, simple conguration, eectively balancing complexity and predictive
power for the non-linear dynamics of the food ination data.
Model evaluation
is study analyzed four dierently congured articial neural network models in order to nd the most
accurate predictive model that can support optimal decision making. In a comparison among the four ANN
models, the study found that ANN [8] and ANN [6] perform better than the other two, with RMSE = 7.10,
MAE = 5.50, and RMSE = 4.17, MAE = 3.4, respectively, for each of these models, provided that the scores are
comparatively lower (Table 9). is testies to the fact that simpler models are better at learning the selected
data compared to models with a higher number of layers and neurons. With a simple model architecture, fewer
neurons, and fewer layers, the model is allowed to learn the dominant patterns (actual signals) because it does
not need to learn every insignicant uctuation that might mislead. e larger model cannot simply learn the
general rule of ination, as it creates unnecessarily complex and wiggly boundaries to t the specic noise over
the training data. When the complex models see new data or test data, those overly complicated parameters fail
to forecast properly, leading to failure. e case also lies in the data selection. Time series data oen relies on
the autoregressive nature of the model for accurate forecasting. Simple models with only one layer of hidden
0.75
1.00
1.25
1.50
1.75
2023 2024 2025
Time
Food Price Index
colour Actual Forecast fill 99.5% PI
ANN [6] Forecast with 99.5% Bootstrap Prediction Intervals
(a
)The figure displays thepoint forecast andthe PredictionI
n-
ter
valfor theFood Price Index (FPI),derived from the ANN [6]
mo
delusing (B=500)bootstrapreplications. The Actual data
(bla
ck line)iscontained withinthe PI, confirmingthe modelsuc-
cessfully
achieved robustcoverage. This 99.5% PI represents a
high
confidence forecastsuitablefor risk assessment.
2015 2020 2025
60 80 100 120140
Comparison plot with TDANN and Prophet models over time
Date
Food Price Index
Original Data
Prophet
Best_ANN
Training End
(b
)Performance comparison of theProphet and Best ANN/ANN
[6
]modelsagainst thedenormalizedFood Price Index (FPI).
The
results highlight thesuperioraccuracyofthe ANN[6] in
capturing fluuctuationsin the data.
Fig. 21. Model performance visualization showing (a) bootstrap-based prediction intervals for the ANN [6]
model and (b) comparative accuracy of ANN [6] and Prophet against the denormalized Food Price Index
(FPI).
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neurons ensure that the model captures the lagged eect properly. Also, the data should have higher frequencies
for more complex neural networks, though the collected data is sucient for the research objectives. e loss
landscape (the terrain the algorithm navigates to nd the lowest error) becomes signicantly more complex and
challenging with two layers.
at is why, additionally, a deep network, LSTM, is built in this study, which is excellent at extracting
high-level abstractions from raw data in the short term (like recognizing a sequence from the past). Adding a
second layer of 14 neurons likely amplies the noise rather than extracting a deeper economic truth. Economic
relationships shi over time with regime changes, so simpler models that capture fundamental, robust trends
generally outperform complex ones that rely on intricate, temporary correlations. Also, the RMSE and MAE
values of both ANN [8] and ANN [6] on the training set are lower than those of the other two: ANN [6, 4] and
ANN [8, 14]. To ensure the total integrity of this research, another time series model, Prophet, which is based on
a completely dierent architectural arrangement, is analyzed to compare its predictive performance with that of
the neural networks. e study nds Prophet has proven to be not so competitive against all four ANN models
in terms of the error measures with RMSE = 11.82 and MAE = 9.88, which are relatively high error margins. On
the contrary, it is also necessary to evaluate how much of the movements of the FPI are explained by the inputs
Fig. 22. Training loss curve for the LSTM model showing convergence behavior over 50 epochs. e loss
(MSE) consistently decreases and stabilizes aer approximately 10 epochs, indicating successful optimization.
No separate validation curve is shown since the model was trained solely on the training dataset, with nal
performance evaluated on the test set.
Parameter Category Value/Description
TARGET_COLUMN Data Food Price Index
TRAIN_RATIO Data Split 0.8 (80% training, 20% testing)
SEQUENCE_LENGTH Data Preparation 3 time steps per sequence
Scaler Type MinMaxScaler (feature_range=(0, 1))
N_FEATURES Model Input Number of columns in df
LSTM Layer 1 Units 64
LSTM Layer 1 Return Sequences TRUE
LSTM Layer 1 Dropout 0.01
LSTM Layer 1 Recurrent Dropout 0
LSTM Layer 2 Units 32
LSTM Layer 2 Return Sequences False (default)
LSTM Layer 2 Dropout 0.01
LSTM Layer 2 Recurrent Dropout 0
Output Layer Type Dense
Output Layer Units 1
Optimizer Training Adam
Loss Function Training Mean Squared Error
Epochs Training 50
Batch Size Training 32
Verbose Training 0 (silent)
Prediction Inversion Scaled back to original units using dummy arrays + inverse_transform
Table 8. LSTM hyperparameter optimization.
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in each of these models, in other words, the goodness of t. Looking at the values of Rsquared, it can be seen in
Table 9 that of these ve models, ANN [6] is the outstanding t in determining the predictions with scores of
0.93, respectively, indicating that external inputs or features can explain 93% variance in the Food Price Index.
Considering ANN [6] as the best model of all TDANNs, the performances of both ANN [6] and Prophet are
visualized on a clean plot against the denormalized FPI series for better readability and rendition (Fig. 21).
Furthermore, in order to nd the best alternative to the TDANN models, the study also built an LSTM
model, a sequential timeseries architecture, which has shown promising results. With RMSE: 4.23 and MAE:
3.47, the LSTM model has demonstrated a relatively low error magnitude in relation to the predicted values,
which is an acceptable level of error. Prediction points across all models studied in this paper are reported in an
organized manner along with their respective intervals in Tables 10,11,12,13,14.
In comparison of the models devised, this study nds that the TDANN, specically, the ANN [6], transcended
the LSTM in both error metrics and model t. e result aligns with a study that used deep learning models
to forecast Consumer Price Index Ination of Food and Beverages, Fuel and Light, and Headline in India,
which suggests that Long Short-Term Memory (LSTM) may not achieve the expected success in forecasting
food ination56. Similar to this study, in a comparative investigation between time series and machine learning
models for forecasting agricultural prices26, have found that ML techniques, perform better in most cases by
using accuracy measures such as Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). A study
on India showed that a simple ANN model with the backpropagation algorithm is highly capable of forecasting
the future values of the monthly Consumer Food Price Index57. In line with this study, results from a paper show
that deep learning models, particularly Long Short-Term Memory (LSTM), outperform ARIMA in capturing
complex temporal patterns, achieving superior accuracy across various error metrics58.
Evaluation Metrics for the SARIMAX, TDANN, Prophet and LSTM
models
Training Testing
Model RMSE
R2
MAE Model RMSE
R2
MAE
SARIMAX 1.024 0.995 0.804 SARIMAX 6.521 0.929 5.739
ANN [8] 1.002 0.995 0.812 ANN [8] 7.106 0.851 5.503
ANN [6, 4] 1.065 0.995 0.876 ANN [6, 4] 8.008 0.792 6.094
ANN [6] 0.876 0.996 0.715 ANN [6] 4.176 0.933 3.400
ANN [8, 14] 1.069 0.995 0.861 ANN [8, 14] 8.175 0.815 6.623
Prophet 0.351 0.999 0.274 Prophet 11.301 0.927 9.404
LSTM 1.281 0.992 1.035 LSTM 4.233 0.831 3.474
Table 9. Evaluation metrics for the proposed models. Note: All metric values are reported in their de-
normalized (original) scale.
Fig. 23. Food Price Index Forecast (July 2022 – March 2025). A comparison of actual Index values against
predictions generated by an LSTM neural network (purple dashed line). e shaded region represents the
prediction uncertainty band.
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A paper compared the deep-learning nonlinear recurrent neural network represented by the LSTM to
the linear ARIMAX model in egg price forecasting in Germany and found that the ARIMAX predictions
consistently underperform compared to the LSTM25. In contrast to the poor performance of the
SARIMAX
in
my study,Yadav59 found that aer employing a convolutional neural network (CNN) and long short-term
memory (LSTM), the ARIMA with exogenous variables (ARIMAX) model performed best in capturing the
inuence of external variables on wheat prices.
Discussion
Predicting food ination is a technically challenging task due to its complex computational mechanism that
is subject to historical subtleties, policy interventions, and governance. In the past, various mathematical
and statistical models have been devised with the aim of achieving better precision and robust analysis in the
research domain of forecasting food prices. However, developing models that employ a nonlinear approach
with neural networks is novel in the eld of economic research, which is evolving rapidly with the development
of AI standards. is paper addresses the understanding of the general price of food, an area of great interest
to economic policymakers and researchers, employing both nonlinear and linear approaches to add new
ndings in this area and achieve satisfactory results. Besides the advantage of handling nonlinear dynamics and
robustness to structural breaks, unlike the classic linear models multicollinearity is not an issue when it comes
to selecting features. However, due to their notoriety of being “black boxes”, it is dicult to understand how they
arrive at a particular forecast. Overtting can be a problem, resulting in inaccurate predictions, which is why
proper regularization is necessary, such as training the model with multiple repetitions or tweaking parameters
Date Actual Predicted Lower Upper
4/1/2022 101.69848 100.21247 98.09685 102.3281
5/1/2022 99.83638 97.48002 94.37364 100.5864
6/1/2022 101.76723 96.31205 92.916 99.70811
7/1/2022 102.19464 96.61209 93.21947 100.00471
8/1/2022 106.15498 102.12155 98.72893 105.51417
9/1/2022 108.42956 103.20069 99.80807 106.59331
10/1/2022 109.51155 103.75817 100.36555 107.15079
11/1/2022 107.8258 104.08448 100.69186 107.4771
12/1/2022 106.6631 103.92647 100.53385 107.31909
1/1/2023 107.42229 102.99432 99.6017 106.38694
2/1/2023 108.25022 103.67578 100.28316 107.0684
3/1/2023 110.01967 104.18503 100.79241 107.57765
4/1/2023 111.26 106.29904 102.90457 109.6935
5/1/2023 109.62 105.45884 102.06293 108.85476
6/1/2023 112.25 107.20414 103.80932 110.59897
7/1/2023 112.74 107.96195 104.56875 111.35516
8/1/2023 120.08 108.485 105.0918 111.87821
9/1/2023 122.47 110.69579 107.30259 114.08899
10/1/2023 123.9 113.697 110.3038 117.09021
11/1/2023 120.04 114.25869 110.86549 117.6519
12/1/2023 117.48 113.98445 110.59124 117.37765
1/1/2024 118.3 114.51733 111.12413 117.91054
2/1/2024 119.07 115.47916 112.08595 118.87236
3/1/2024 121.5 117.52433 114.13112 120.91753
4/1/2024 122.63 118.79572 115.36948 122.22195
5/1/2024 121.42 118.12073 114.65777 121.58369
6/1/2024 123.94 119.14436 115.67038 122.61834
7/1/2024 128.64 119.84784 116.37636 123.31931
8/1/2024 133.72 122.39609 118.92462 125.86757
9/1/2024 135.21 123.63921 120.16773 127.11068
10/1/2024 139.58 125.85501 122.38354 129.32648
11/1/2024 136.61 126.95519 123.48372 130.42666
12/1/2024 132.65 126.93008 123.45861 130.40156
1/1/2025 130.97 127.17435 123.70288 130.64583
2/1/2025 130.08 127.54182 124.07034 131.01329
3/1/2025 132.35 129.12271 125.65123 132.59418
Table 10. SARIMAX predictions on test data with 95% condence bounds.
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and keeping simpler architectures. e temporal dependencies of the time series were addressed by including
lagged features, which also contributed to improving the prediction accuracy. e best two TDANN models
discussed in this paper have successfully acknowledged the pitfalls and satisfactorily produced predictions that
yield deviations of less than 6% in RMSE and MAE.
is paper’s ndings align with results from similar previous studies that analyzed monthly economic data,
supporting the conclusion that the feedforward articial neural network with backpropagation modeling, which
does not assume linearity, excels at solving complex problems and outperforms traditional econometric models
in forecasting accuracy60–62.
On the contrary, the study introduced Facebook’s Prophet, a popular forecasting method in business research,
to showcase whether the piecewise linear or the non-linear approach is better at predicting the movement of a
highly sensitive price index. Prophet is popular for its user-friendly service that decomposes the predictions or
forecasts into their distinct components, allowing users to clearly see the contribution of each component, a huge
advantage for communicating results to a non-technical audience or for a research paper where interpretability
is key. It is also ecient at handling outliers or missing data, common problems in real-world datasets like the
food price index. Nevertheless, Prophet is vulnerable to highly volatile data subject to frequent uctuations not
based on the trend and seasonality assumptions, and too many additional regressors can cause overtting.
LSTM models are computationally intense and complex compared to simpler traditional RNNs or feed-
forward networks. is leads to slower training. ey are inherently sequential, meaning they process data
step by step. Also, having a large number of hyperparameters makes the LSTM sensitive to subtle changes,
which is why tuning the model is challenging and time-consuming. Furthermore, LSTMs are oen considered
black-box models. It is dicult to interpret the role of the cell state and the gates to understand why the model
Date ANN [8] ANN [6, 4] ANN [6] ANN [8, 14] Actual
5/1/2022 97.95025 91.97274 98.04269 94.30254 99.83638
6/1/2022 100.4026 99.6302 99.81741 97.98769 101.76723
7/1/2022 102.1059 103.4127 101.5747 100.5601 102.19464
8/1/2022 102.0145 105.9124 104.3186 101.192 106.15498
9/1/2022 104.888 104.9349 106.9766 102.7552 108.42956
10/1/2022 102.9775 104.8618 105.6047 101.9238 109.51155
11/1/2022 106.1497 107.2111 107.0137 107.2266 107.8258
12/1/2022 107.1158 107.367 107.7119 108.2716 106.6631
1/1/2023 105.5196 107.1394 106.333 108.6211 107.42229
2/1/2023 107.4401 108.779 105.9312 108.4497 108.25022
3/1/2023 106.6969 108.0342 107.1094 106.9629 110.01967
4/1/2023 109.4615 108.6603 107.0897 106.4248 111.26
5/1/2023 107.9234 109.2033 108.6521 106.5494 109.62
6/1/2023 109.0033 106.8699 109.9809 106.4009 112.25
7/1/2023 110.0778 113.6989 110.6534 108.9772 112.74
8/1/2023 110.0212 109.2136 112.8393 108.5654 120.08
9/1/2023 113.8936 115.6623 117.7543 112.2658 122.47
10/1/2023 112.1192 115.3659 117.3439 112.5598 123.9
11/1/2023 120.0586 119.1005 122.9912 117.1823 120.04
12/1/2023 116.4391 116.5459 119.7116 116.076 117.48
1/1/2024 111.3577 116.1248 117.7941 118.2796 118.3
2/1/2024 114.2564 117.1827 116.6095 117.5227 119.07
3/1/2024 112.0553 117.4598 115.4891 115.6915 121.5
4/1/2024 113.1374 110.9263 113.3996 110.7825 122.63
5/1/2024 116.8563 106.3568 116.7154 111.95 121.42
6/1/2024 116.4591 110.5674 118.8934 112.3733 123.94
7/1/2024 118.0015 119.4121 123.3423 117.1618 128.64
8/1/2024 115.6572 117.4274 131.0849 117.5377 133.72
9/1/2024 122.4577 121.0514 131.472 119.4438 135.21
10/1/2024 125.1832 123.1583 133.4077 122.2107 139.58
11/1/2024 130.4462 124.8342 135.5943 124.4024 136.61
12/1/2024 122.1313 121.9903 131.3094 124.3932 132.65
1/1/2025 124.9566 122.8675 128.7592 125.4466 130.97
2/1/2025 127.5101 123.3335 124.8028 125.8629 130.08
3/1/2025 130.2158 121.85 121.9395 122.4735 132.35
Table 11. TDANN-based point predictions of food price index.
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made a specic prediction. Still, the model built for this study is devised according to industry practice and is
functionally sound for forecasting Food Price Index.
erefore, this study has strategically selected the features that are associated with changes in the Food Price
Index and equipped the model smoothly, having very low error margins in every benchmark.
ough the models perform prociently by every metric, solid predictive modeling is not a panacea for time
series analysis of all food prices. TDANN and LSTM are very acceptable in predicting or forecasting future
price trends of economic data, but in a rational world, the turn of both domestic and global events can shape
the trend, nullifying predictions. Shocks from regional war in some part of the world to political tension within
a community can shi the prices of agricultural and manufactured foods, and edible items abruptly. Hence,
predictive analysis of a price index should not be held absolute, given there are only a limited number of external
inputs considered. A study by Kirikkaleli and Darbaz63explored the causality and relationships between U.S.
food prices, energy prices, economic policy uncertainty, and the value of the U.S. dollar and found that the dollar
price negatively aects the food price index at both high and low volatility periods, implying a signicant positive
relationship between the energy price index and the food price index. Moreover, the study stated that energy is a
long-run and permanent cause of the food price index.Weinberg and Bakker64 utilized a domestic-level measure
of food prices rather than the world market price and found a positive and signicant relationship between food
prices and outbreaks of social unrest and conict across several countries. A study by MacLachlan et al.65 used
the optimal and kitchen-sink SARIMAX forecasting models and oered strong evidence that changes in food-
at-home CPI signicantly correlate to prior changes in core CPI and the money supply.
Date y/Actual yhat/Predicted yhat_lower yhat_upper
4/1/2022 101.69848 100.3272 99.88872 100.79123
5/1/2022 99.83638 98.61918 98.16091 99.11495
6/1/2022 101.76723 99.08383 98.46601 99.60032
7/1/2022 102.19464 100.6309 99.96317 101.158
8/1/2022 106.15498 102.3544 101.40097 102.83868
9/1/2022 108.42956 104.1363 102.91592 104.7691
10/1/2022 109.51155 104.9491 103.39878 105.74081
11/1/2022 107.8258 104.8006 102.92912 105.82971
12/1/2022 106.6631 104.8763 102.73333 106.21209
1/1/2023 107.42229 105.4623 103.06059 107.11597
2/1/2023 108.25022 105.3809 102.6193 107.42456
3/1/2023 110.01967 105.7414 102.87645 108.26026
4/1/2023 111.26 105.7604 102.28095 108.6462
5/1/2023 109.62 104.2885 100.40494 107.52865
6/1/2023 112.25 104.6107 100.12557 108.23148
7/1/2023 112.74 106.2565 101.25976 110.22782
8/1/2023 120.08 107.6046 102.09583 112.1171
9/1/2023 122.47 109.4486 103.2826 114.18383
10/1/2023 123.9 110.1883 103.58882 115.50424
11/1/2023 120.04 110.3463 102.8802 116.12083
12/1/2023 117.48 110.5643 102.42882 116.90159
1/1/2024 118.3 110.9782 102.68678 118.07871
2/1/2024 119.07 110.8076 101.88953 118.72931
3/1/2024 121.5 111.0294 101.21062 119.08975
4/1/2024 122.63 111.6023 100.95518 120.17496
5/1/2024 121.42 109.6687 97.93309 118.66248
6/1/2024 123.94 110.4165 98.0491 119.97279
7/1/2024 128.64 111.605 98.82693 121.9366
8/1/2024 133.72 113.2043 99.81022 124.2723
9/1/2024 135.21 115.3087 101.45656 126.80403
10/1/2024 139.58 116.3793 101.69517 128.55834
11/1/2024 136.61 115.9287 100.73605 128.57533
12/1/2024 132.65 115.6746 99.75886 128.8686
1/1/2025 130.97 116.4115 100.00263 130.2233
2/1/2025 130.08 116.4957 99.1808 131.00175
3/1/2025 132.35 116.7667 98.52899 131.87587
Table 12. Prophet forecast values with prediction intervals.
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us, the author recommends the inclusion of exchange rate, money supply, and social unrest in any future
studies of food ination or food price indices in the context of Bangladesh.
e future scope of research is very broad in that data of dierent frequencies with other features or variables
can be incorporated with dierent models to strengthen forecasting literature. Demographic data, which is not
considered in this research, can be an essential component for analyzing and forecasting a Food Price Index
because consumer behavior, which is driven by demographic characteristics, directly impacts the demand side of
food markets. Especially, the price of food items is very susceptible to the location of a population in Bangladesh,
since urban consumers are the net consumers relying on a complicated supply chain, exposed to price
uctuations, whereas the rural population generally has easier access to food they grow. Simultaneously, factors
aecting the food economy from various aspects of the global supply chain, food security, natural disasters,
urbanization, industrialization, and land use can be taken into consideration for further research. Researchers
can also utilize other machine learning models like MLP, XGBoost, and VARMAX, which are prevalent in the
forecasting discipline and can rival ANN and Prophet, illuminating new ndings.
A study predicting food price ination points to a decline in the production of most food crops, especially
rice and wheat, in South Asia by 2050 due to climate change66. e results from the environmental Global Trade
Analysis Project model indicate that the unfavorable increased heat impacts on agricultural productivity (crop,
land, and labor) will reduce food production and create upward pressure on food prices in Nepal, Pakistan,
Bangladesh, and Sri Lanka, mirroring the ndings of the non-linear models discussed in this study. It will lead
to a reduction in household food consumption, posing a threat to regional food security. An investigation67
used the Dynamic Common Correlated technique and found that climate change reduces food availability and
increases the risk of food insecurity in South Asia. Another study identied changes in fuel prices, money supply,
and fertilizer prices as key drivers of food ination in Sri Lanka68, a striking similarity to the learnings of the
macroeconomic oscillations of Bangladesh. Likewise, one signicant paper found that real and nominal frictions,
as well as structural shocks, have become more pronounced, and ination is now driven more by cost-push and
Date Actual Predicted Lower Upper
7/1/2022 102.1946442 100.2888148 91.99056743 108.5870621
8/1/2022 106.1549818 101.2760305 92.97778316 109.5742778
9/1/2022 108.4295606 102.960249 94.66200163 111.2584963
10/1/2022 109.5115547 104.4553841 96.15713679 112.7536315
11/1/2022 107.8257959 107.7195601 99.42131278 116.0178074
12/1/2022 106.6631006 108.5880793 100.289832 116.8863266
1/1/2023 107.4222898 107.5543868 99.2561395 115.8526342
2/1/2023 108.2502246 106.3650503 98.066803 114.6632977
3/1/2023 110.0196735 106.6452186 98.34697131 114.943466
4/1/2023 111.26 107.3825128 99.08426549 115.6807602
5/1/2023 109.62 108.2508903 99.95264292 116.5491376
6/1/2023 112.25 109.4336806 101.1354333 117.731928
7/1/2023 112.74 110.6271149 102.3288676 118.9253623
8/1/2023 120.08 112.2874942 103.9892469 120.5857416
9/1/2023 122.47 115.0643008 106.7660535 123.3625481
10/1/2023 123.9 117.1501965 108.8519492 125.4484438
11/1/2023 120.04 120.5633351 112.2650878 128.8615825
12/1/2023 117.48 120.5120551 112.2138078 128.8103025
1/1/2024 118.3 120.0473007 111.7490534 128.3455481
2/1/2024 119.07 118.1768854 109.8786381 126.4751327
3/1/2024 121.5 117.2671438 108.9688964 125.5653911
4/1/2024 122.63 117.5790569 109.2808095 125.8773042
5/1/2024 121.42 119.43004 111.1317927 127.7282874
6/1/2024 123.94 121.7165327 113.4182854 130.0147801
7/1/2024 128.64 123.3400837 115.0418364 131.6383311
8/1/2024 133.72 125.5970417 117.2987943 133.895289
9/1/2024 135.21 128.1017337 119.8034864 136.399981
10/1/2024 139.58 131.2281257 122.9298784 139.526373
11/1/2024 136.61 133.9305541 125.6323067 142.2288014
12/1/2024 132.65 133.699881 125.4016337 141.9981284
1/1/2025 130.97 132.9964578 124.6982105 141.2947052
2/1/2025 130.08 131.0573019 122.7590546 139.3555492
3/1/2025 132.35 129.8685388 121.5702915 138.1667862
Table 13. LSTM output: point predictions and 95% condence intervals.
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demand shocks in India69, a neighboring country of Bangladesh, in the aermath of the COVID-19 pandemic
and the Russia-Ukraine war. All the changes taking place in dierent parts of South Asia collectively attest to
the delayed eects on historical food prices in Bangladesh. From these latest studies centered on South Asian
countries, the author can infer that the factors aecting the food prices in these countries work homogenously,
like how they work for Bangladesh.
Policy implications
e policy implications are based on the SHAP dependence and interaction analysis, the decomposed Prophet
components, and the rising ination trend captured by the TDANN and LSTM models, all informed by author’s
economics knowledge.
• Invest in ood control infrastructure (e.g., improved drainage, protective embankments) for high precipita-
tion regimes and irrigation expansion/drought-resistant crops for low precipitation regimes, especially during
the critical April-July rice harvesting season.
• Adjust the size and location of national grain reserves (rice and wheat) based on the prior precipitation read-
ing. Boost reserves when MP_lag3 is in the extreme zones to prepare for market uncertainty and potential
supply shortfalls that drive prices up.
• Subsidize or develop weather-indexed crop insurance linked directly to the critical MP_lag3 thresholds. It will
help stabilize farmers’ income and reduce overall supply risk.
Time Forecast Lower Upper Actual
5/1/2022 0.9290035 0.7600376 1.0319921 0.9638373
6/1/2022 0.963469 0.8751186 0.9976705 1.0013351
7/1/2022 0.9975965 0.901148 1.0584146 1.0096356
8/1/2022 1.0508832 0.9391627 1.1000099 1.0865466
9/1/2022 1.1025017 0.948763 1.1363395 1.1307196
10/1/2022 1.0758605 0.9454024 1.112583 1.1517323
11/1/2022 1.1032231 0.9953232 1.1670282 1.1189943
12/1/2022 1.1167819 0.9657068 1.1959633 1.0964144
1/1/2023 1.0900046 0.9291478 1.168685 1.1111581
2/1/2023 1.0822009 0.9802948 1.1565027 1.1272369
3/1/2023 1.1050807 0.9632147 1.2078196 1.1616001
4/1/2023 1.1046995 0.9605629 1.2144433 1.1856876
5/1/2023 1.1350405 0.9813591 1.2064863 1.1538383
6/1/2023 1.1608469 0.9880603 1.2263859 1.2049138
7/1/2023 1.1739064 1.0239603 1.2484835 1.2144297
8/1/2023 1.2163587 0.9769246 1.258667 1.3569748
9/1/2023 1.3118083 1.0514717 1.3704131 1.4033893
10/1/2023 1.3038382 1.0563335 1.3488948 1.4311603
11/1/2023 1.4135105 1.0626604 1.5855337 1.356198
12/1/2023 1.3498198 1.0384502 1.5566088 1.306482
1/1/2024 1.3125824 0.8646376 1.544266 1.3224066
2/1/2024 1.2895773 1.0356682 1.455259 1.3373603
3/1/2024 1.2678177 0.9901753 1.4991223 1.3845516
4/1/2024 1.2272395 0.8525365 1.4783737 1.4064966
5/1/2024 1.2916335 0.9428624 1.4908067 1.382998
6/1/2024 1.3339297 0.947513 1.5070285 1.4319372
7/1/2024 1.4203301 1.0613581 1.4941117 1.5232126
8/1/2024 1.570694 1.0069943 1.6721943 1.6218678
9/1/2024 1.5782111 1.0839197 1.7043902 1.650804
10/1/2024 1.6158032 1.1066315 1.7931271 1.7356708
11/1/2024 1.6582666 0.9759244 1.9316423 1.6779925
12/1/2024 1.5750526 1.0110576 1.850628 1.601088
1/1/2025 1.5255268 1.0165658 1.8912166 1.5684619
2/1/2025 1.4486924 1.0848416 1.732403 1.5511779
3/1/2025 1.3930872 1.057502 1.7676138 1.595262
Table 14. ANN [6] Forecast Points with Bootstrap Prediction Intervals.
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• Deploy food reserves or import taris only when the model indicates that extreme delayed precipitation or
rainfall is leading to a strong positive inuence on current FPI (signaling acute supply issues), focusing mar-
ket intervention precisely when the weather shock breaks the normal pattern.
• Maintain transparent communication during extreme weather events to manage public and market expec-
tations.
• Embed the Energy Price Index and Lagged Food Price Index interaction directly into national budget plan-
ning and trade decisions to mitigate ination risk before it materializes. When prior food ination is already
high, the government should proactively hedge a greater portion of its projected energy and key agricultural
input imports (like fertilizer, which is energy-intensive). is guarantees a lower cost base for the EPI com-
ponent of the supply chain, ensuring that even if global energy prices spike, the domestic ination amplier
is disarmed.
• Not letting the businesses justify raising prices based on past inationary pressure by strategically stabilizing
or subsidizing energy costs when the risk of high food prices is present.
• Adopt a dual-approach strategy that combines proactive short-term supply management with long-term
structural support. e Trading Corporation of Bangladesh (TCB) should use predictive models to build up
stocks of high-demand goods (sugar, oil, and dairy) months in advance. ey should then sell these goods
through Open Market Sales (OMS) two weeks before festivals to keep prices from going up too much when
demand is high.
• Policy should focus on reducing the baseline cost of production by lowering import duties on animal feed and
providing low-interest nancing for modern livestock farming, ensuring price stability in beef and poultry
markets year-round.
e implications outlined here are formulated for policymakers, researchers, and relevant public agencies
overseeing food security, agricultural and irrigation planning, climate-risk management, and the administration
of grain reserves and trade interventions.
Conclusion
is study was initiated to address the historical rise in food ination at an alarming rate, as reported by the
World Bank, and to explore multiple facets impacting food prices, which are concerning Bangladesh’s economy.
Secondary data from highly prestigious sources comprising ve time series variables with 177 entries for each
are processed for building econometric and machine learning models. e author has satisfactorily established
SARIMAX, TDANN, Prophet, and LSTM models to ll the identied research gap in food ination prediction.
e model performances reect the true integrity of the data selection and robustness in judgment.
Although SARIMAX is one of the classic time series linear models in the forecasting domain, given the
complex interactions between historical data on climate factors, energy prices, and food prices, it was not a good
t compared to the non-linear models. is nding supports the paper’s hypothesis that a non-linear approach
is superior to the traditional linear approach, as non-linear research using machine learning models yields better
results in detecting the volatile movements of food ination.
ough ANN [6] and LSTM came out as the choice models compared to the others, the evaluation metrics
for ANN [8] also show highly signicant results, making it equally relevant and best alternative. is testies in
favor of the articial neural networks’ eciency in capturing the underlying intricacy within the inputs and the
target.
While LSTM models are oen preferred for sequence or time-series data due to their ability to capture
long-term dependencies, the TDANN in this comparison performed better according to the specic evaluation
metrics. is could suggest that the dataset did not have strong, long-term sequential patterns that would
signicantly benet the LSTM architecture, or perhaps the TDANN was better tuned. Besides, LSTM is a deep
learning model demanding large timeseries data with higher frequencies (daily, hourly, etc.) for operating
complex analysis. ough it has received moderately lower errors in predictions, the Rsquared value (0.83)
suggests, this may not be the best model for the chosen data, a nding identied as a limitation of this study.
e underperformance of the LSTM suggests that monthly food ination in this context may be characterized
by ‘short memory’ dynamics. While analysis attributed LSTM results to noise amplication, it is also highly
probable that the economic drivers of monthly ination are dominated by immediate, short-term shocks rather
than long-term dependencies. Consequently, the complex gated mechanisms of the LSTM, designed to capture
long-range temporal patterns, may be less eective than simpler models when the data lacks signicant long-
term memory.
e author suggests preferring TDANN over LSTM to forecast food prices considering weather shocks and
energy market volatility to mitigate the rising food ination and to support policy interventions. Backed by a
strong
R2
value, the TDANN prediction points are close to the actual values, eciently capturing the future data
trend and accurately modeling its spikes and drops.
In addition to the insights from these two models, Prophet has provided valuable information on how
holidays temporarily inuence the prices of essential goods. Prophet components analysis sheds light on the
passive inuence of supply shocks on prior agricultural vulnerability, as cost-push ination drives prices up. It
directly makes the ndings in SHAP analysis more credible.
erefore, this paper has met all the stated objectives, followed by hypothesized research questions with
evidence-based assertions.
e nal verdict on both ANN [6] and LSTM: Are these models strong enough for policy interventions?
Major shocks typically move prices by 10% to 30% (a jump of 12–35 points). ANN [6] and LSTM’s error is
only 3.4% (4 points). e predictions will successfully catch the big wave even if the exact height is slightly o.
e model successfully identies extreme deviation events within a 3.6% margin of error. e models serve
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as a dependable warning system. Because the models’ errors are signicantly smaller than the magnitude of
true structural shocks, both architectures can reliably distinguish genuine crisis events from normal market
uctuations (1–3%). e model prioritizes responsiveness to shocks over smoothing, ensuring we don’t miss a
crisis event.
So, within the context of shock detection and short-term monitoring, the evidence supports the use of
TDANN and LSTM models as reliable tools to inform timely policy interventions.
Monthly data, sucient for conventional time-series techniques and moderately parameterized neural
networks, limits the eectiveness of deeper sequential architectures, such as LSTMs. With relatively few
observations, highly complex models may fail to fully exploit their representational capacity, potentially leading
to unstable generalization or limited gains over simpler alternatives. Access to higher-frequency data, such as
weekly or daily food price series at the district and regional level, would likely enable the extraction of other
temporal patterns and more reliable training of deep learning models. In addition, although the proposed
methodological framework is broadly transferable, the estimated importance and policy implications should
be interpreted with caution when extending the ndings to other economies, as dierences in agricultural
structures, subsidy mechanisms, market integration, and climate conditions may alter them.
e global supply chain of energy markets is highly dynamic subject to uncertain global events like war,
pandemic, exchange rate, taris, etc. As highly demanding natural resources such as oil, gas, and electricity
experience drastic changes in price and production, these uctuations can directly trigger domestic production
cost, which lead to disrupting stable food ination. On top of that, extreme weather events that function beyond
human control, such as oods and drought are proven to be impacting the prices forward in time. erefore,
major evaluations of existing environmental policies are essential, and evidence-based policy recommendations
will aid in monitoring the Food Price Index going forward.
is research addresses the critical gap in food ination literature by providing a multifaceted investigation
with deep interpretability for policy design, categorized into three core contributions. First, methodologically,
the study rigorously compares traditional linear econometric and generalized additive frameworks (SARIMAX
and Prophet) against advanced non-linear machine learning and deep learning architectures, including TDANN
and LSTM. By evaluating these models on the same monthly dataset, the research validates the hypothesis
that non-linear models are better equipped to capture the complex, volatile movements of food ination that
traditional approaches oen fail to detect. Second, the empirical contribution for Bangladesh involves the
development of a unique domestic-level model that integrates the synergistic eects of climate variables and the
Energy Price Index on the Food Price Index. Utilizing a specialized dataset, this study captures regional market
dynamics and vulnerabilities specic to a nation consistently highlighted on the World Bank’s ination Red
List. Finally, the policy contribution through XAI lies in the application of SHAP to decode the best one among
the TDANN models. Moving beyond “black-box” predictions, this analysis transforms complex forecasts into
actionable, quantitative insights regarding the specic drivers of weather shocks and energy market volatility
that have historically impacted food price ination. is technique leveraged feature importance to translate
high-accuracy forecasts into specic and targeted policy implications for managing weather shocks and risks in
Bangladesh’s agricultural input and energy markets.
is paper has established ML models based on empirical results, following the mathematical theories of
time-series forecasting, with the notion of contributing to the existing macroeconomic literature that will serve
the readership of policy analysts, economists, academic researchers, and government stakeholders.
Data availability
All datasets used in this study are publicly available from ocial repositories, and no proprietary data were used.
Detailed source information and access links are provided in the Supplementary File.
Code availability
Available.
Received: 18 September 2025; Accepted: 1 January 2026
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