From Feature Selection to Forecasting: A Two-Stage Hybrid Framework for Food Price Prediction Using Economic Indicators in Turkey

1. Introduction

Food price volatility has emerged as a critical challenge for emerging economies, with significant implications for both macroeconomic stability and social welfare. The interconnected nature of modern economic systems implies that food prices are influenced not only by traditional agricultural factors but also by complex interactions with diverse economic sectors including healthcare, communication services, and financial markets. Understanding and predicting these price movements has become essential for effective economic policy formulation, particularly in emerging economies facing high inflation volatility (Karagöl, 2023). This is increasingly recognized as a cornerstone of economic and social sustainability, where food security underpins equitable development and resilience against systemic shocks.

In Turkey, food price dynamics hold particular significance as the Food and Non-Alcoholic Beverages Consumer Price Index (CPI) group represents approximately 25% of the national CPI basket as of 2024. Recent empirical evidence demonstrates that food price fluctuations create cascading effects throughout economic systems, influencing macroeconomic variables such as economic growth, employment levels, and income distribution patterns (Özçelik & Uslu, 2024). The Turkish Statistical Institute's classification of food prices within the CPI framework underscores the systemic importance of developing accurate forecasting models for these price movements (Eştürk & Albayrak, 2018).

Traditional econometric approaches to food price analysis have predominantly focused on supply-side factors and historical price patterns, often failing to capture the complex cross-sector interdependencies that characterize modern economies. While machine learning techniques offer promising alternatives for capturing non-linear relationships and complex interactions among economic variables (Baumeister & Kilian, 2014), limited research has systematically compared traditional econometric methods with modern machine learning approaches within a unified analytical framework or explored optimal prediction windows for timely policy interventions.

This research addresses these critical gaps by developing a comprehensive two-stage methodology that first systematically identifies key economic drivers through multiple econometric techniques, then evaluates ten different approaches for forecasting accuracy. Using monthly data spanning 2017-2024 from the Central Bank of Turkey and the World Food Programme database, this study provides both theoretical insights into inflation transmission mechanisms and practical tools for economic forecasting. The primary contributions include demonstrating how diverse economic indicators collectively influence food price dynamics, establishing the superiority of ensemble methods for economic forecasting, and providing empirical evidence for optimal prediction frameworks with direct policy implications for emerging economy contexts.

2. Literature Review

The literature on food price prediction using economic indicators and machine learning techniques has expanded significantly in recent years. The reviewed studies can be categorized under two headings: relationship and causality and prediction models.

Table 1 summarizes key findings from the literature review across these categories:

These studies provide valuable insights into the application of various statistical methods and machine learning techniques for analyzing economic data and predicting food prices. They highlight different approaches to feature selection, model development, and evaluation metrics that have guided the current research.

3. Methodology

3.1. Research Framework

This study employs a two-stage analytical framework: Stage 1 systematically identifies economic drivers affecting overall food prices through CPI analysis; Stage 2 validates these drivers through pilot application to rice price prediction, providing a scalable methodology for broader food price forecasting applications.

3.2. Data Collection and Preprocessing

3.2.1. Dataset Creation

The dataset was created by including Dollar Sale, Euro Sale, Gold Bullion Sale prices, and the entire CPI group from the Electronic Data Delivery System (EVDS) of the Central Bank of the Republic of Turkey. The data spans from 2017 to 2024, providing a comprehensive time period for analysis. (EVDS, 2024)

Rice was selected as the pilot case due to its status as a staple food for over half of the world's population (Muthayya et al., 2014) and extensive documentation of its price volatility relationships with macroeconomic indicators (Valera, 2022). Rice prices are obtained from World Food Programme database. The city is selected as Ankara, Turkey to assure data consistency. (World Food Programme Price Database, 2024)

3.2.2. Data Preprocessing

For effective use in analytical applications, Min-Max normalization was applied to the data:

X_normalized = (X - X_min) / (X_max - X_min)

This normalization technique is widely adopted in machine learning applications to ensure equal scaling of variables with different ranges (Hastie et al., 2009). Missing value analysis revealed only the "103.POST-SECONDARY AND PRE-UNIVERSITY EDUCATION" CPI group with 106 missing values, which was removed due to minimal expected impact on food products.

3.3. Relationship and Causality Analysis

The relationship and causality analysis phase aims to systematically identify which economic indicators have significant relationships with food prices, following the methodological approaches established in recent econometric literature.

3.3.1. Time Series Analysis and Stationarity Testing

Partial Autocorrelation Function (PACF) analysis was conducted to measure direct effects of the relationship between an observation and its lagged values in the time series (Box et al., 2016). This technique helps determine the appropriate lag structure for autoregressive models by identifying the direct correlation between current and past values:

PACF(k) = corr(Xt, Xt-k | Xt-1, Xt-2, ..., Xt-k+1)

Augmented Dickey-Fuller (ADF) Test was used to check for stationarity in the data series, as required for causality testing (Dickey & Fuller, 1979). The test examines the presence of unit roots in time series:

Δyt = α + βt + γyt-1 + δ1Δyt-1 + ... + δp-1Δyt-p+1 + εt

Where the null hypothesis H0: γ = 0 (unit root exists) versus H1: γ < 0 (stationary). This test is crucial for ensuring the validity of subsequent causality analyses, as non-stationary series can lead to spurious regression results.

3.3.2. Correlation Analysis

Three different correlation methods were employed to identify variables influencing the food CPI, providing complementary perspectives on variable relationships (Cohen et al., 2003):

Pearson Correlation measures linear relationships between variables:

r = Σ[(xi - x̄)(yi - ȳ)] / √[Σ(xi - x̄)²Σ(yi - ȳ)²]

This parametric measure is most appropriate when variables follow normal distributions and relationships are linear.

Spearman Rank Correlation captures monotonic relationships regardless of linearity:

ρ = 1 - (6Σdi²) / [n(n² - 1)]

This non-parametric approach is robust to outliers and suitable for variables that may not meet normality assumptions.

Kendall's Tau provides robust association measure based on concordant and discordant pairs:

τ = (C - D) / [n(n-1)/2]

Where C and D represent concordant and discordant pairs, respectively. This measure is particularly useful for small sample sizes and provides more reliable inference.

3.3.3. Lag Features Analysis

Lag correlation analysis was performed for previous months, creating lagged features for all columns and calculating correlations with the target variable using all three correlation methods. This approach helps identify optimal temporal relationships and leads/lags in the data, which is crucial for understanding how economic indicators influence food prices over time (Baumeister & Kilian, 2014).

3.3.4. Granger Causality Test

After stabilizing the dataset, Granger causality tests were applied to identify causal relationships between variables (Granger, 1969). This approach has been successfully used in food price studies to establish predictive relationships (Cerveny, 2023):

yt = α0 + Σ(i=1 to p) αiyt-i + Σ(i=1 to p) βixt-i + εt

Where rejection of H0: β1 = β2 = ... = βp = 0 indicates x Granger-causes y. This test determines whether past values of economic indicators contain information useful for predicting food prices beyond what is contained in past values of food prices alone.

3.3.5. Autoregressive Distributed Lag (ARDL) Model

The ARDL analysis examined relationships from both short-term and long-term perspectives, following the methodology established by Pesaran et al. (2001). This approach has been particularly effective in food price analysis, as demonstrated by Özçelik and Uslu (2024):

yt = α + Σ(i=1 to p) βiyt-i + Σ(i=0 to q) γixt-i + εt

The model considered 12-month lags for the food CPI and 1-month lags for other items. ARDL models are advantageous because they can handle variables with different orders of integration and provide both short-run dynamics and long-run equilibrium relationships.

3.3.6. Cointegration Test (Engle-Granger)

The cointegration analysis tested for long-term relationships between non-stationary series using the two-step Engle-Granger method (Engle & Granger, 1987). This technique is essential for identifying stable long-run relationships between economic variables, as applied in similar studies examining price relationships (Ozpolat, 2020):

Step 1: yt = α + βxt + ut (estimate long-run relationship)

Step 2: Test residuals for stationarity to confirm cointegration

Cointegration testing helps distinguish between spurious and genuine long-term relationships among economic variables.

3.3.7. Random Forest Feature Importance

Random Forest feature importance scores were used to identify variables with the strongest relationship to the target variable, employing both random 80%/20% split and chronological split approaches (Breiman, 2001). This machine learning-based approach complements traditional econometric methods and has shown effectiveness in feature selection for economic forecasting applications.

3.3.8. Attribute Shortlist

According to previous study, we aim to combine all studies best performed items with selecting top two items from each relationship and causality study. Since some top performers might be same so that we have a workable shortlist.

3.4. Predictive Model Development

Based on the relationship analysis results, ten key predictor variables were identified for food price prediction. Multiple prediction models were then developed and compared for their forecasting performance, following the comparative modeling approach established in recent food price prediction literature (Atalan, 2023).

3.4.1. Linear Regression

Linear regression serves as the baseline model for comparison, testing the fundamental assumption of linear relationships between economic indicators and food prices (Hastie et al., 2009):

Y = β₀ + β₁X₁ + β₂X₂ + ... + βₚXₚ + ε

β̂ = (X'X)⁻¹X'Y

Despite its simplicity, linear regression often provides competitive performance in economic forecasting and offers excellent interpretability for policy makers.

3.4.2. Random Forest

Random Forest combines multiple decision trees using bootstrap aggregating to capture non-linear relationships and interactions between variables (Breiman, 2001). This ensemble method has demonstrated superior performance in agricultural price prediction, as shown by Atalan (2023) for Turkish milk price forecasting:

ĥᵦ(x) = Σᵢ₌₁ⁿ wᵢ(x)yᵢ

ĥ_RF(x) = (1/B) Σᵦ₌₁ᴮ ĥᵦ(x)

VI(Xⱼ) = (1/B) Σᵦ₌₁ᴮ Σₜ p(t)[ΔI(t)]I(v(t) = j)

Where B is the total number of trees, and VI represents variable importance. The model's ability to provide feature importance rankings makes it valuable for understanding which economic indicators most strongly influence food prices.

3.4.3. Gradient Boosting

Gradient Boosting sequentially combines weak learners to minimize residual errors, building upon the boosting framework developed by Friedman (2001). This method excels at capturing complex patterns in economic data:

F(x) = Σₘ₌₁ᴹ γₘhₘ(x)

Fₘ(x) = Fₘ₋₁(x) + γₘhₘ(x)

rᵢₘ = -[∂L(yᵢ, F(xᵢ))/∂F(xᵢ)]_{F=Fₘ₋₁}

Where γm is the step size and rim are pseudo-residuals. The sequential error correction mechanism makes gradient boosting particularly effective for economic time series with complex underlying patterns.

3.4.4. XGBoost

XGBoost implements an optimized gradient boosting framework with regularization techniques to prevent overfitting (Chen & Guestrin, 2016). This algorithm has gained widespread adoption in economic forecasting due to its robust performance:

L(θ) = Σᵢ l(yᵢ, ŷᵢ) + Σₖ Ω(fₖ)

Ω(f) = γT + (1/2)λ||w||²

L̃⁽ᵗ⁾ = Σᵢ₌₁ⁿ [gᵢfₜ(xᵢ) + (1/2)hᵢfₜ²(xᵢ)] + Ω(fₜ)

Where Ω(f) represents regularization terms. The built-in regularization and efficient implementation make XGBoost suitable for economic datasets with high dimensionality.

3.4.5. Support Vector Regression (SVR)

SVR uses ε-insensitive loss function for robust predictions against outliers, which is particularly valuable in economic data that often contains extreme values (Vapnik, 1995):

f(x) = Σᵢ₌₁ⁿ (αᵢ - αᵢ*)K(xᵢ, x) + b

K(xᵢ, xⱼ) = exp(-γ||xᵢ - xⱼ||²)

min (1/2)||w||² + C Σᵢ₌₁ⁿ (ξᵢ + ξᵢ*)

The kernel approach allows SVR to capture non-linear relationships while maintaining robustness to outliers, making it suitable for volatile economic indicators.

3.4.6. Long Short-Term Memory (LSTM)

LSTM addresses vanishing gradient problems in RNNs and is designed to capture long-term dependencies in time series data (Hochreiter & Schmidhuber, 1997). Deep learning approaches like LSTM have shown promise in agricultural price prediction (Ji et al., 2022):

fₜ = σ(Wf · [hₜ₋₁, xₜ] + bf)

iₜ = σ(Wi · [hₜ₋₁, xₜ] + bi)

C̃ₜ = tanh(WC · [hₜ₋₁, xₜ] + bC)

Cₜ = fₜ * Cₜ₋₁ + iₜ * C̃ₜ

oₜ = σ(Wo · [hₜ₋₁, xₜ] + bo)

hₜ = oₜ * tanh(Cₜ)

The gate mechanisms allow LSTM to selectively remember and forget information, potentially capturing complex temporal patterns in economic relationships.

3.4.7. Artificial Neural Networks (ANN)

ANNs use backpropagation for learning complex non-linear patterns between economic indicators and food prices (Rumelhart et al., 1986):

yⱼ = f(Σᵢ wᵢⱼxᵢ + bⱼ)

wᵢⱼ(t+1) = wᵢⱼ(t) - η ∂E/∂wᵢⱼ

Multi-layer perceptrons can approximate complex non-linear functions, making them suitable for modeling intricate economic relationships.

3.4.8. ARIMA

ARIMA models time series using autoregressive and moving average components, representing the classical approach to time series forecasting (Box et al., 2016). Similar seasonal models have shown success in short-term food price predictions (Wanjuki et al., 2022):

φ(B)(1-B)ᵈXₜ = θ(B)εₜ

(1-φ₁B-...-φₚBᵖ)(1-B)ᵈXₜ = (1+θ₁B+...+θᵩBᵩ)εₜ

While ARIMA focuses solely on temporal patterns, it provides a benchmark for comparing the added value of incorporating economic indicators.

3.4.9. NARX-RNN

NARX networks model nonlinear dynamic systems with exogenous inputs, combining temporal dependencies with external economic factors (Lin et al., 1996):

y(t) = f(y(t-1), y(t-2), ..., y(t-nᵧ), u(t-1), u(t-2), ..., u(t-nᵤ))

h(t) = tanh(Wᵧᵧh(t-1) + Wᵤᵧu(t) + Wᵧᵧy(t-1) + b)

y(t) = Wᵧᵧh(t) + bᵧ

The model was tested with different lag periods (3, 6, 9, and 12 months) to find optimal prediction windows. This approach bridges traditional econometric modeling with neural network capabilities.

3.4.10. ANFIS

ANFIS combines fuzzy logic with neural networks, providing interpretable non-linear modeling (Jang, 1993):

x = A, Y= B ise z = px + qy + r ;

μₐᵢ(x) = exp(-(x-cᵢ)²/2σᵢ²)

wᵢ = μₐᵢ(x) × μᵦⱼ(y)

w̄ᵢ = wᵢ/Σᵢwᵢ

w̄ᵢfᵢ = w̄ᵢ(pᵢx + qᵢy + rᵢ)

Output = Σᵢw̄ᵢfᵢ

Due to architectural constraints, ANFIS was limited to the two highest-ranked features from the feature selection process. The fuzzy rule-based approach offers transparency in decision-making processes.

3.4.11. SHAP-Based Ensemble Interpretability

To enhance model transparency and uncover consensus-driven economic drivers, SHAP (SHapley Additive exPlanations) analysis was applied to the three top-performing models: Gradient Boosting, Random Forest, and Support Vector Regression (SVR). SHAP values provide a game-theoretic approach to explain the output of machine learning models by quantifying each feature’s marginal contribution to individual predictions (Lundberg et al., 2020; Lundberg & Lee, 2017). Given the small dataset size (n = 94), KernelSHAP was employed for SVR (which lacks native tree-based SHAP support), while TreeSHAP was used for Gradient Boosting and Random Forest for computational efficiency and exact Shapley value estimation. The analysis was conducted on the full test set (n = 19) using a representative background sample to ensure stable explanations. Feature importance was derived as the mean absolute SHAP value across all test instances, enabling cross-model comparability and consensus ranking.

3.5. Model Evaluation

3.5.1. Evaluation Metrics

Models were evaluated using an 80-20 train-test split with three performance metrics that provide complementary perspectives on prediction accuracy:

• Mean Absolute Error (MAE):

MAE = (1/n) Σ|yi - ŷi|

• Root Mean Squared Error (RMSE):

RMSE = √[(1/n) Σ(yi - ŷi)²]

• Coefficient of Determination (R²):

R² = 1 - (SSres / SStot)

These metrics enable comprehensive assessment of model performance, with MAE providing interpretable average error, RMSE penalizing larger deviations, and R² indicating explained variance.

3.5.2. Cross-Validation Assessment

To ensure robust model evaluation and detect potential overfitting, K-fold cross-validation is implemented for the top-performing model. K-fold cross-validation partitions the dataset D into k equal folds, where each model fᵢ is trained on k-1 folds and tested on the remaining fold Dᵢ. The cross-validation score is computed as:

CV_Score = (1/k) Σᵢ₌₁ᵏ Pᵢ

Where Pᵢ represents the performance score on fold i. This methodology provides robust performance estimates and enables detection of overfitting by assessing model stability across different data partitions (Hastie et al., 2009).

3.5.3. Statistical Significance Test

To assess whether performance differences between top-performing models were statistically meaningful, paired t-tests were conducted using cross-validation scores. For models i and j with CV scores xᵢ and xⱼ, the paired t-test evaluates:

H₀: μᵢ - μⱼ = 0 (no difference)

H₁: μᵢ - μⱼ ≠ 0 (significant difference)

t = (x̄ᵢ - x̄ⱼ) / (sᵈ/√n)

Where sᵈ is the standard deviation of paired differences and n is the number of CV folds. This approach provides robust statistical inference for model selection decisions (Hastie et al., 2009).

4. Relationship and Causality Analyses & Results

4.1. Time Series Analysis

Time series analysis was conducted to observe the changes in the 'TP FG J011' (CPI food index) value over the last 10 years. The analysis revealed a significant increase, especially during the pandemic period. However, this increase follows a trend, with a notable difference between the trend until the end of 2021 and the trend afterward. This provides a suitable basis for examining the precursor causes.

4.2. Partial Autocorrelation Function (PACF)

PACF analysis was used to measure the direct effects of the relationship between an observation and its lagged values in the time series. When performing this test for the correlation of the "TP FG J011" column with previous months, it was observed that it only has a direct relationship with the previous month.

4.3. Correlation Analysis

To identify other items that influence the "TP FG J011" dependent variable, three different correlation methods were used: Pearson, Spearman, and Kendall methods. Tables 2, 3, and 4 show the top three items with the highest correlation values for each method.

As shown in Table 2, household-related CPI components demonstrate the strongest Pearson correlation with food prices, suggesting shared underlying economic factors.

Table 3 reveals that service-oriented CPI components show strong rank-based correlations with food prices, indicating similar monotonic relationships with underlying economic conditions.

Kendall's tau correlation results in Table 4 confirm the findings from the Spearman correlation analysis, with service-related CPI items showing the strongest associations with food prices.

The combined correlation results in Table 5 provide a more comprehensive view, highlighting both household maintenance services and non-alcoholic beverages as having the strongest overall correlation with food prices.

4.4. Lag Features Analysis

A lag correlation analysis was performed for previous months. The analysis created lagged features for all columns and calculated correlations with the target variable using all three correlation methods.

As shown in Table 6, a one-month lag of household appliances prices demonstrates the strongest correlation with current food prices, suggesting a potential leading indicator relationship.

4.5. Stationarity Test

The Augmented Dickey-Fuller (ADF) test was used to check for stationarity in the data series, which is required for some causality relationship tests. The test showed that all data series were non-stationary, necessitating a data transformation process to achieve stationarity.

4.6. Granger Causality Test

After stabilizing the dataset, Granger causality tests were applied to identify causal relationships between variables. Items with p-values less than 0.05 indicated significant causal relationships with food prices at specific lag months.

4.7. Autoregressive Distributed Lag (ARDL) Model

The ARDL analysis examined the relationship between the dependent variable and multiple independent variables from both short-term and long-term perspectives. The model considered 12-month lags for 'TP FG J011' and 1-month lags for other items.

The ARDL results in Table 7 highlight that healthcare-related CPI components and telecommunication services have significant statistical relationships with food prices, controlling for other factors.

4.8. Cointegration Test (Engle-Granger)

The cointegration analysis tested for long-term relationships between non-stationary series.

The cointegration test results in Table 8 indicate strong long-term relationships between food prices and education, social protection, and transportation costs.

4.9. Random Forest Feature Importance Analysis

Random Forest feature importance scores were used to identify variables with the strongest relationship to the target variable. Two approaches were used: random 80%/20% split and chronological split.

The Random Forest analysis in Table 9 highlights insurance, medical products, and transport services as having the most predictive importance for food prices.

4.10. Analysis Results & Attribute Shortlist

The analyses identified ten key factors taking two best performing items from each Relationship and Causality analysis that have the most significant influence on the "TP FG J011 FOOD" CPI item, along with their most influential month lag:

As summarized in Table 10, healthcare-related items, communication services, house items, and education costs emerged as the most influential predictors for food prices in Turkey.

Based on the optimal lag periods identified in the relationship and causality analysis (Table 10), temporal features were constructed for each predictor. Specifically:

- TP FG J053 (Household Appliances): 1-month lag

- TP FG J073 (Transportation Services): 6-month lag

- TP FG J011 (Food CPI): 1-month lag (based on PACF analysis)

- All other predictors: Current period (0-month lag)

These lagged features were consistently applied across all predictive models except NARX-RNN, which internally optimizes temporal dependencies. For ARIMA, which does not accommodate exogenous variables with mixed lag structures, only the autoregressive component of TP FG J011 was utilized.

5. Prediction Model Development & Results

5.1. Dataset Preparation

Using the identified features from previous analyses, a combined dataset was constructed for the price prediction model. Rice prices from the World Food Programme database were selected as a pilot case due to rice being a staple food item with price volatility that can be analyzed in relation to economic indicators. The dataset included both Turkish Lira (TL) and US Dollar (USD) prices, though only TL-based prices were considered for modeling purposes.

The target variable (Rice TL prices) and features were separated, and Min-Max normalization was applied to ensure that all variables were on the comparable scale. This preprocessing step was particularly important when using economic indicators with different value ranges to prevent any single variable from dominating the model based solely on its scale.

5.2. Model Selection and Implementation

Based on the literature review, several models were selected and implemented to predict rice prices. Each model was evaluated using a train-test split of 80%-20% respectively. The performance was assessed using Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and coefficient of determination (R²). The following models were implemented: Linear Regression, Random Forest, XGBoost, Support Vector Regressor (SVR), Long Short-Term Memory (LSTM), Artificial Neural Network (ANN), Gradient Boosting Regressor, ARIMA, NARX-RNN (with varying lag periods), ANFIS (Adaptive Neuro-Fuzzy Inference System).

5.3. Model Performance Results

The performance metrics for each model are summarized in Table 11.

As shown in Table 11, the Gradient Boosting model significantly outperformed other models across all evaluation metrics.

5.4. Model-Specific Findings

5.4.1. Linear Regression

The linear regression model provided a high R² score of 0.9915, indicating that a linear model is quite effective in explaining the data. This suggests that rice prices have a linear relationship with the selected features. The model's success demonstrates that economic indicators can produce reasonable short to medium-term predictions using linear relationships.

5.4.2. Random Forest

The Random Forest algorithm produced a high R² value of 0.9976, successfully capturing complex relationships in the dataset. Beyond its predictive performance, the model's feature importance capability offered insights into which factors most significantly influence rice prices.

5.4.3. XGBoost

XGBoost delivered strong performance with an R² of 0.9975. The gradient boosting technique effectively modeled non-linear relationships between economic indicators and rice prices, demonstrating its ability to capture complex factors affecting price fluctuations.

5.4.4. Support Vector Regressor (SVR)

The SVR model achieved an impressive R² value of 0.9982 with relatively low error metrics. These results indicate the model's effectiveness in understanding complex relationships between economic indicators and rice prices, making it one of the top-performing approaches.

5.4.5. LSTM

Contrary to expectations, the LSTM model underperformed significantly with a negative R² value (-5.4817), indicating difficulty in explaining the variance in the target variable. This performance issue may be attributed to dataset size limitations, the complexity of the temporal structure, or hyperparameter selection. The results suggest that deep learning models may require larger datasets to show their full potential.

5.4.6. Artificial Neural Network (ANN)

The ANN model achieved a high R² value of 0.9903, demonstrating its ability to learn the non-linear and complex relationships between economic indicators and rice prices. However, its relatively higher RMSE compared to other models suggests the presence of some larger deviations.

5.4.7. Gradient Boosting

The Gradient Boosting model outperformed all others with the lowest MAE and RMSE values, and the highest R² score (0.9990). This exceptional performance demonstrates the model's ability to capture complex interactions between features and minimize errors through sequential tree-building.

5.4.8. ARIMA

The ARIMA model yielded a negative R² value (-0.7834), indicating that the model is not suitable for this dataset. This result suggests that rice prices have complex relationships that cannot be explained by time dimensions alone, highlighting the importance of including multiple factors beyond time in economic data analyses.

5.4.9. NARX-RNN

The NARX-RNN model was tested with different lag periods (3, 6, 9, and 12 months) to find the optimal prediction window. The results are presented in Table 12.

Table 12 demonstrates that a 6-month lag period provides optimal predictive performance for the NARX-RNN model, suggesting this timeframe best captures the economic relationships affecting rice prices.

5.4.10. ANFIS

The ANFIS model, which combines fuzzy logic with neural networks, showed limited success with an R² value of 0.3497. Due to the model's structure, only the two highest-ranked features from the feature selection process were used: household appliances (TP FG J053) and furniture and related items (TP FG J051). The model's relatively poor performance indicates that these two features alone are insufficient for accurate price prediction.

The relatively poor performance of the ANFIS and LSTM models is attributed to the limited data volume and feature dimensionality, which restrict the convergence capability of deep or hybrid architectures. These models typically require larger, more diverse datasets to capture complex non-linear dependencies effectively.

5.4.11. SHAP Interpretability Insights

SHAP Analysis was conducted to detect most important attributes for the prediction models. Top 5 items which have major impact on rice price prediction is shared in the Table 13.

SHAP analysis revealed both model-specific and consensus-level insights into the economic determinants of rice prices in Turkey. While individual models assigned varying importance weights, a robust cross-model consensus emerged around four key predictors:

• TP FG J125 (Insurance) consistently ranked among the top-2 features across all three models (avg. rank: 2.03), suggesting that household risk-mitigation expenditures are strongly coupled with food price dynamics.
• TP FG J062 (Outpatient Services) and TP FG J073 (Transportation Services) appeared in the top-3 of at least two models and within the top-5 of all three, reinforcing the role of healthcare accessibility and logistics costs in food inflation transmission.
• TP FG J051 (Furniture & Furnishings) showed high stability, ranking 2nd in Random Forest and 5th in both Gradient Boosting and SVR.

Notably, the lagged food CPI (TP FG J011) which is the 7^th item having 0.97 average SHAP importance of the SHAP feature list, exhibited moderate influence in SVR and Random Forest but low importance in Gradient Boosting, indicating that exogenous economic indicators may dominate autoregressive effects in ensemble models. The lowest consensus was observed for TP FG J124 (Social Protection) and TP FG J127 (Other Services), which ranked 9th–10th across models.

Spearman correlation analysis of feature rankings revealed moderate agreement between models (ρ ≈ 0.47–0.52, p > 0.1), suggesting complementary but non-redundant interpretability perspectives. The average SHAP importance across models provides a robust, ensemble-weighted indicator of true economic influence, reducing model-specific bias.

5.5. Model Robustness Assessment

5.5.1. Cross Validation

Given the exceptional performance of the top-ranked Gradient Boosting model (R² = 0.9990, MAE = 0.2838), 5-fold cross-validation analysis was conducted to assess potential overfitting concerns. Cross-validation results are shown in Table 14.

The moderate variance (standard deviation = 0.0324) indicates acceptable model stability across different data partitions. The difference between the single-split test (R² = 0.9990) and cross-validation mean (R² = 0.9742) is 0.0248. The training performance on the original 80% split (R² = 0.9992) was nearly identical to test performance (R² = 0.9990), with a minimal gap of 0.0002, confirming excellent generalization without overfitting validating the reliability of the Gradient Boosting approach for food price prediction applications.

Similarly, when we conducted Cross Validation with 5-fold for top 3 performed models, the results shared in Table 15. The results validate top performed models reliability and show their equivalence of representing predictions.

Cross-validation means were: SVR (0.9896 ± 0.0168), Random Forest (0.9811 ± 0.0208), and Gradient Boosting (0.9742 ± 0.0324). Although SVR demonstrated the highest cross-validation mean and lowest variance, Gradient Boosting achieved superior single-split test performance (R² = 0.9990 vs. 0.9982 for SVR). This suggests that while SVR exhibits more consistent performance across data partitions, Gradient Boosting may better capture specific patterns in the test period. Importantly, statistical testing confirms, the statistical analysis confirms that all three methods demonstrate excellent and statistically equivalent performance for rice price prediction.

5.5.2. Statistical Significance Test

Paired t-tests based on 5-fold cross-validation scores (α = 0.05) were conducted to evaluate whether performance differences between the top three models were statistically significant.

Statistical analysis revealed no significant differences between any pair of models (all p > 0.05), indicating statistically equivalent performance despite ranking differences in single-split evaluation. Statistical Significance Test Results shared in Table 16.

6. Discussion

This study presents a novel two-stage machine learning framework that systematically integrates econometric feature selection with predictive modeling to forecast food prices in Turkey, a critical task given the country’s high inflation volatility and the substantial weight of food in its CPI basket. The results offer compelling evidence that food price dynamics are not driven solely by agricultural or supply-side factors but are closely intertwined with in cross-sectoral economic interdependencies.

6.1. Feature Selection and Economic Interconnectedness

The relationship and causality analyses revealed a complex network of linkages between food prices and seemingly unrelated sectors. Ten key predictors were identified through a consensus approach that combined Pearson’s, Spearman’s, and Kendall’s correlation analyses, Granger causality, ARDL modeling, cointegration tests, and Random Forest feature importance. Notably, healthcare-related indicators such as Outpatient Services (TP FG J062) and Medical Products (TP FG J061) emerged as statistically significant drivers in both short- and long-run frameworks. This finding challenges conventional inflation models that treat food and health expenditures as independent and instead suggests that cost pressures in the healthcare sector may spill over into food markets, possibly through labor costs, logistics, or household budget reallocation.

Similarly, Transportation Services (TP FG J073) and Insurance (TP FG J125) were consistently ranked among the top predictors across multiple methodologies. The strong influence of transport costs aligns with established economic theory on supply chain transmission, while the prominence of insurance expenditures points to a broader household risk-management behavior that co-moves with food consumption patterns, particularly relevant in high-inflation environments where financial uncertainty is elevated.

Perhaps most striking is the identification of Education Programmes (TP FG J105) and Social Protection (TP FG J124) as cointegrated with food prices, indicating a long-term equilibrium relationship. This implies that structural social expenditures may serve as macroeconomic anchors or leading indicators of consumption stress, offering policymakers early signals of impending food inflation.

6.2. Predictive Performance and Model Robustness

In the forecasting stage, ensemble methods, particularly Gradient Boosting, Support Vector Regression (SVR), and Random Forest, demonstrated exceptional predictive accuracy (R² > 0.997), significantly outperforming both classical time series models (e.g., ARIMA) and deep learning architectures (e.g., LSTM, NARX-RNN). The failure of ARIMA (R² = –0.78) underscores the inadequacy of univariate time-series approaches in capturing the multidimensional drivers of food inflation in emerging economies. Likewise, the poor performance of LSTM (R² = –5.48) highlights the limitations of deep learning models when applied to small, noisy economic datasets without sufficient regularization or domain-informed architecture design.

The NARX-RNN model, however, provided a critical insight: a 6-month lag yielded optimal predictive performance, suggesting that exogenous economic shocks require approximately half a year to propagate through Turkey’s supply chains and manifest in consumer food prices. This temporal window has direct policy relevance; it implies that early warning systems based on leading indicators (e.g., transport costs, healthcare inflation) can provide actionable foresight for monetary and fiscal interventions.

Cross-validation and statistical significance testing further validated the robustness of the top models. Although Gradient Boosting achieved the highest point performance (R² = 0.9990), paired t-tests confirmed that its advantage over SVR and Random Forest was not statistically significant (p > 0.05), indicating equivalent predictive reliability across these ensemble methods. This equivalence enhances practical flexibility: policymakers may choose models based on interpretability (Random Forest), robustness to outliers (SVR), or sequential error correction (Gradient Boosting).

6.3. Interpretability and Policy Implications

SHAP-based interpretability analysis bridged the technical and economic narratives by revealing a cross-model consensus on the dominant role of Insurance, Outpatient Services, and Transportation Services in shaping rice price dynamics. The consistent high ranking of insurance expenditures, a proxy for household financial vulnerability, suggests that food inflation in Turkey is not merely a market phenomenon but a reflection of broader socio-economic vulnerability. This insight supports the integration of social safety nets into inflation-mitigation strategies.

Moreover, the moderate correlation (ρ ≈ 0.47–0.52) between model-specific feature rankings indicates that each algorithm captures complementary aspects of the underlying economic system. The ensemble-weighted SHAP importance thus offers a more holistic and less biased view of true economic influence than any single model could provide.

7. Conclusion

This study bridges econometric rigor with machine learning innovation to address a pressing challenge in emerging economies: accurate and interpretable food price forecasting. By developing a two-stage framework that first identifies causally and statistically relevant economic indicators and then evaluates a diverse set of predictive models, we demonstrate that food inflation in Turkey is deeply intertwined with sectors beyond agriculture, including healthcare, transportation, education, and household financial services.

Our findings yield three key contributions. First, we provide empirical evidence of cross-sectoral inflation transmission mechanisms, revealing that cost pressures in services can significantly influence food prices, a phenomenon underexplored in traditional macroeconomic models. Second, we establish the superiority and statistical equivalence of ensemble machine learning methods (Gradient Boosting, SVR, Random Forest) over both classical econometric and deep learning approaches for small-sample economic forecasting, offering a practical toolkit for central banks and planning agencies. Third, through SHAP-based interpretability and lag-structure analysis, we identify a six-month policy window for intervention and highlight insurance, healthcare, and transportation as high-leverage indicators for early warning systems.

These results carry direct implications for inflation targeting, social protection design, and supply chain resilience in volatile emerging markets. Future research could extend this framework to other food commodities or countries, incorporate real-time data streams, or integrate structural breaks (e.g., currency crises) into the modeling architecture. Nevertheless, the present work lays a robust foundation for data-driven, interdisciplinary approaches to food price stability and macroeconomic resilience.