A Time-Series Hybrid Multi-Model Machine Learning Framework for Staple Crops Yield Prediction

1. Introduction

Agriculture is essential for achieving global food security and economic stability, particularly in developing countries [1,2]. As the world population is expected to reach 9.7 billion by 2050 [3], enhancing crop productivity is crucial for meeting future food requirements. Crops such as rice, wheat, maize, corn, and soybeans are vital to the world’s food supply and are significant exports [4,5,6,7,8]. Precise crop yield predictions allow governments and organizations to make educated decisions about resource management and trade strategies. Prior yield estimation techniques, such as surveys, expert evaluations, or trend-based models, frequently lack prompt updates and flexibility, particularly when confronted with rapidly changing climate conditions [9]. This has propelled the movement towards data-driven strategies utilizing machine learning (ML), deep learning (ML), internet of things (IoT), and artificial intelligence (AI) to reveal intricate, non-linear connections in crop, soil, and environmental information [10,11,12]. ML models like support vector regression (SVR), k-nearest neighbors (KNN), decision tree (DT), gradient boosting (GB) and random forest (RF) have surpassed traditional regression methods in recent usages [13,14].

1.1. Need of Yield Prediction

Food is a necessity for every human being on this planet. The crop yield prediction system determines which crop needs to be grown in which season and in which year. However, many farmers commit suicide because they are unable to decide which crop yield is suitable for this year. Farmers are facing unfavorable weather conditions and lower yield predictions. The combination of ML, DL, and IoT will help address this critical issue, enabling farmers to predict which crops are suitable for the current season.

1.2. Problem Statement

Accurate crop yield forecasting is critical for agricultural plannings, food distribution formulation, and market stability. Traditional statistical models such as ARIMA and ETS assume linearity and stationarity, which limits their ability to capture nonlinear and nonstationary agricultural yield patterns influenced by climate variability, technological change, and management practices. Recent studies have applied ML and DL models; however, most existing works:

• Focus on single-model approaches.
• Are restricted to short-term forecasting horizons.
• Ignore yield instability and volatility characteristics.
• Lack systematic comparison across statistical, ML, and DL models.

Therefore, there is a need for a comprehensive hybrid-forecasting framework that integrates statistical ML, and DL techniques to improve long-term crop yield forecasting accuracy and robustness.

1.3. Contribution of the Study

This study makes the following key contributions:

• Proposes a unified hybrid artificial intelligence framework combining statistical ML and DL models for crop yield forecasting.
• Performs a systematic comparison of classical models (ARIMA, ETS), volatility-based models (Generalized autoregressive conditional heteroscedasticity (GARCH family)), ML models (ANN, support vector machine (SVM), partial least squares (PLS)), and deep learning models (long-short term memory (LSTM)).
• Introduces signal decomposition-based hybrid models (Wavelet-ANN and empirical mode decomposition (EMD)-ANN) to handle nonstationary yield series.
• Incorporates yield instability and heteroscedasticity diagnostics using Cuddy–Della Valle Index (CDVI) and autoregressive conditional heteroscedasticity- lagrange multiplier (ARCH-LM) tests.
• Evaluates model performance using various performance evaluation metrics root mean squared error (RMSE), mean absolute error (MAE), r-squared (R²), and mean absolute percentage error (MAPE).
• Generates long-term (20-year) forecasts for multiple crops, which are rarely addressed in existing literature.

2. Literature Review

Researchers employed various ML approaches to estimate crop yields. [13] developed a web application for crop recommendation and yield estimation. They used ML classification and regression techniques for crop recommendations and yield estimation. [15] proposed a novel system for crop yield prediction that utilizes crop yield data, meteorological data, and ML techniques. They evaluated KNN, GB, and multivariate logistic regression, achieving a remarkable R² of 99.99%. [16] used AI in agriculture for crop optimization and yield prediction with KNN, SVM, and XGBoost algorithms. [14] had proposed machine learning models for yield prediction and crop classification, attaining a high accuracy of 99.7% for classification and 99.9% for yield prediction. [17] utilized regression models such as random forest, decision tree, XGBoost, and deep learning (convolution neural network (CNN), LSTM) for predicting crop yields in India. [18] had developed a crop recommendation framework based on XAI, utilizing historical crop yields and soil nutrients. [19] Additionally, a crop recommendation framework based on XAI was introduced, achieving an R² value of 0.94152. [20] used a reinforcement learning model to predict the yield of the crop. [21] forecasted the crop yield using ensemble learning on synthetic data generated by Prophet, used ET as a meta model, and XGB, RF, KNN, and decision tree (DT) as weak learners. [22] employed Terra\MODIS-derived metrics to estimate crop yield in Canadian Prairies, especially when vegetation indices such as EVI2 are applied. Barley, canola, and spring wheat yields were better predicted by EVI2 than by NDVI, with relative root mean square error (RRMSE) values at the Census Agriculture Region level ranging from 14% to 20%. [23] proposed a framework for crop yield prediction named Flyer, which was based on edge computing and federated learning for agriculture 5.0. [24] used a Bayesian-optimized gated recurrent unit (GRU) for the enhancement of crop yield prediction. When compared to conventional methods, experimental results demonstrate the significant improvement in yield forecasting achieved by the proposed IQ-GRU framework for both mid-season and season-end predictions. The goal of [25] was to determine the optimal crop prediction model to assist farmers in selecting crops based on soil nutrients and climate. The study compared the RF, DT, and KNN algorithms using the Gini and Entropy criteria, and found that RF achieved the highest accuracy. The CrYP tool, developed by [26], operates within the google earth engine (GEE) framework, enabling spatially detailed predictions of crop yields. This open-source application enhances the accuracy of yield forecasts, which is crucial for ensuring food security and effective agricultural management. [27,28,29,30,31] studied corn yield prediction. [27] used ML and statistical tools for improving the corn Nitrogen recommendation tool by utilizing soil and weather data information. The study by [31] focused on a parametric yield model and semiparametric neural networks for forecasting corn crop yield. [28] Utilized neural network methods for predicting the yield of corn, achieving an accuracy of 98%. [30] Ensemble different ML models to predict the corn yield and achieved an RRMSE of 9.5% (with an optimized weighted ensemble model). The authors of [29] used leaf area and the normalized difference vegetation index to predict corn yield, obtaining an accuracy of 94%. [8,32,33,34,35] investigated various ML and DL techniques to predict soybean yield. [32] Conducted the study on corn and soybean yield prediction in Canada using ANN MLP (multi-layer perceptron). [8] designed a deep learning CNN_LSTM model to predict the yield of soybean using CONUS country-level data from 2003 to 2015. [33] used deep learning and multimodal data fusion techniques to predict soybean crop yield data collected from UAVs. [35] had combined weather data and ML techniques to improve the soybean crop yield prediction in southern Brazil. [34] Employed a CNN and an LSTM model to predict the yield of soybeans in the USA. The dataset used in this study was collected from NASA’s and GEE. The authors of [36] predicted soybean yield using a CNN LSTM-ViT (vision-transformer) model by utilizing remotely sensed data and earth observations. [37] enhanced maize yield predictions in the Kaffa Zone of Southwestern Ethiopia by utilizing geographic information systems (GIS) and remote sensing technology data. These approaches provide precise and rapid data, which is essential for farmers’ and governments’ informed decision-making. Research has indicated a strong association between maize production and NDVI, with correlations as high as 89% when rainfall data is included. Strong prediction abilities have been demonstrated by models created using satellite data, which have an R² of 0.89 and an root mean squared error (RMSE) of 1.54 q/ha. [38] demonstrated a statistical framework for corn and soybean yield prediction using ensemble ML models. The obtained result shows an average accuracy of 80% for corn and 81% for soybean. [39] predicted the cotton crop yield using RF, SVR, MLR, and LightGBM models. The RF regressor achieved a highest accuracy of 97.75%. [40] used weather parameters to predict the cotton crop yield from 2005 to 2020. The proposed model random forest extreme gradient achieved RMSE of 0.05. [4] presented a unique method (Gaussian kernel regression) for rice yield prediction using SAR and optimal imaginary data. [41] proposed a new LSTM-based model for rice yield prediction. The developed model was known as target aware yield prediction (TAYP). The TAYP model achieved an accuracy of 95%. [42] used wheat crop for yield prediction using the climate NDVI data fusion technique. [5] presented a framework for wheat yield prediction using least absolute shrinkage and selection operator (LASSO), RF, and XGB models of ML based on remote sensing data. [43] Predicted the yield of the Sugarbeet crop using a temporal graph neural network and a multimodal meta-transfer model. [44] focused on a comprehensive review of Palm oil yield prediction using ML models. [45] employed data fusion and deep learning to predict the yield of the tea crop, achieving an R-squared of 0.99. The comparative analysis of staple crops are demonstrated in Table 1.

3. Methods and Materials

3.1. Dataset Description

The study uses secondary time-series data on crop yields collected from officially published agricultural statistics (https://ourworldindata.org/grapher/key-crop-yields). The dataset consists of annual yield observations (tons per hectare) for multiple major crops over several decades.

• Temporal coverage: Multiple decades (annual frequency)
• Spatial scope: International-level aggregated crop yields
• Data type: Time-series
• Source: Government agricultural databases - UNFAO (2025)
• Dependent Variable: Crop yield (tonnes per hectare)
• Independent Variables:
  • Lagged crop yield values (time-lag features)
  • Decomposed components (trend and residuals from Wavelet and EMD)
  • Volatility measures (for GARCH-based models)
    • Climatic and economic variables are not explicitly included; instead, their effects are implicitly captured through temporal yield dynamics.

3.2. Preprocessing Steps

• Handling missing values using interpolation
• Normalization for machine learning and deep learning models
• Train–test split (80:20) preserving temporal order

3.3. Proposed Solution

This study proposes a hybrid forecasting framework that:

• Combines linear, nonlinear, and deep temporal representations.
• Captures trend, volatility, and nonlinear dependencies.
• Provides robust long-term yield forecasts.

Unlike earlier studies, the framework handles no stationarity explicitly and selects best-performing models’ crop-wise. The methodology employed in this study involved evaluating a diverse set of statistical and machine learning models for forecasting crop yield across multiple crops shown in Figure 1.

3.4. Model Selection

The following time series model are used for crop yield prediction.

ARIMA

The ARIMA (p, d, q) model represents crop yield as a function of its past values and past error terms.

Yₜ = c + φ₁Yₜ₋₁ + φ₂Yₜ₋₂ + … + φₚYₜ₋ₚ

+ θ₁εₜ₋₁ + θ₂εₜ₋₂ + … + θ_qεₜ₋q + εₜ

Where: Yₜ = crop yield at time t, φᵢ = autoregressive parameters, θⱼ = moving average parameters, εₜ = white noise error term, c = constant

ETS

The additive ETS model is expressed as:

Yₜ = lₜ₋₁ + bₜ₋₁ + εₜ

lₜ = lₜ₋₁ + bₜ₋₁ + αεₜ

bₜ = bₜ₋₁ + βεₜ

Where: lₜ = level component, bₜ = trend component, α, β = smoothing parameters, εₜ = error term

ANN

The ANN model predicts crop yield as:

Ŷₜ = f(Σ wᵢXᵢ + b)

Where: Xᵢ = input variables (lagged yields), wᵢ = weights, b = bias, f() = nonlinear activation function, Ŷₜ = predicted yield

LSTM

LSTM captures long-term dependencies using memory cells.

Forget gate: fₜ = σ(W_f[hₜ₋₁, xₜ] + b_f)

Input gate: iₜ = σ(W_i[hₜ₋₁, xₜ] + b_i)

Cell update: Cₜ = fₜCₜ₋₁ + iₜtanh(W_c[hₜ₋₁, xₜ] + b_c)

Output gate: oₜ = σ(W_o[hₜ₋₁, xₜ] + b_o)

Hidden state: hₜ = oₜtanh(Cₜ)

Wavelet–ANN

Wavelet decomposition splits the yield series into components:

Yₜ = Aₜ + Σ Dₜᵢ

Where: Aₜ = approximation component, Dₜᵢ = detail components. The ANN is trained using Aₜ as input to predict future yield.

EMD–ANN

EMD decomposes the series into intrinsic mode functions:

Yₜ = Σ IMFᵢ + rₜ

Where: IMFᵢ = intrinsic mode functions, rₜ = residual trend. The ANN uses the trend component rₜ for forecasting.

ETS–ANN

The hybrid ETS–ANN model is defined as:

Yₜ = Ŷₜᴱᵀˢ + Ŷₜᴬᴺᴺ

Where: Ŷₜᴱᵀˢ = ETS forecast, Ŷₜᴬᴺᴺ = ANN forecast of ETS residuals

PLS

PLS projects predictors and response into latent space:

X = TPᵀ + E

Y = UQᵀ + F

Where: T, U = latent scores, P, Q = loading matrices, E, F = residuals

3.5. Performance Evaluation Metrics

The evaluation metrics used for crop yield prediction is:

Mean Absolute Error (MAE):

MAE = (1/n) Σ |Yₜ − Ŷₜ|

Root Mean Square Error (RMSE):

RMSE = √[(1/n) Σ (Yₜ − Ŷₜ)²]

Coefficient of Determination (R²):

R² = 1 − [Σ(Yₜ − Ŷₜ)² / Σ(Yₜ − Ȳ)²]

Mean Absolute Percentage Error (MAPE):

MAPE = (100/n) Σ |(Yₜ − Ŷₜ)/Yₜ|

For yield instability measure Cuddy–Della Valle Index (CDVI) is used.

CDVI = CV × √(1 − R²)

Where: CV = coefficient of variation, R² = goodness of fit from trend regression

The objective was to assess predictive performance comprehensively across linear time-series models, nonlinear machine learning architectures, and hybrid methods that combine elements of both. Among the models considered were ARIMA, LSTM, ANN, EMD-ANN, Wavelet-ANN, ETS-based hybrids such as ETS-ANN, ETS-LSTM, ETS-SVM, as well as Partial Least Squares (PLS). Each model was trained on historical crop yield data and validated using out-of-sample test sets to ensure comparability. Hyperparameter tuning was conducted using appropriate techniques: ARIMA relied on information criterion-based order selection, neural network architectures such as ANN and LSTM were optimized via iterative validation, while hybrid ETS approaches integrated exponential smoothing with neural network or support vector components. Forecasting performance was quantified using multiple error metrics: MAE, RMSE, coefficient of determination (R²), MAPE, Crop-Dependent Variability Index (CDVI), and residual diagnostics for ARCH effects. This multi-metric evaluation ensured that models were compared not only on point forecast accuracy but also on their ability to explain variance, control relative errors, and capture volatility.

4. Results and Analysis

Table 2 provide aggregate results across all crops demonstrate clear differences in model performance. When ranked by mean MAE (mean absolute error) across all crops, PLS emerged as the most accurate with an average MAE of 0.1420 and RMSE of 0.1756, paired with a near-zero R² value of -0.1161. This suggests PLS consistently produced low forecast errors but did not yield positive explained variance values relative to the mean baseline, highlighting the difficulty of achieving high variance explanation in agricultural time-series data. Hybrid exponential smoothing approaches also performed strongly: ETS-ANN, ETS-LSTM, and ETS-SVM all achieved an average MAE of 0.1988 and RMSE of 0.2218, with MAPE around 3.06 percent. These models maintained moderate error rates while providing staple forecasts across crops. LSTM as a standalone neural network achieved an average MAE of 0.2226 and RMSE of 0.2588, with a MAPE of 3.69 percent. Although its R² was negative (-0.7609), it ranked favorably in error-based comparisons, outperforming ARIMA.

ARIMA, as the classical statistical benchmark, produced an average MAE of 0.3437 and RMSE of 0.3786, with MAPE around 4.93 percent. Its R² mean was -2.2886, indicating limitations in capturing variance. Nonetheless, ARIMA outperformed several nonlinear and hybrid models in error terms, underscoring the continued relevance of linear models in yield forecasting. In contrast, models such as ANN, EMD-ANN, and Wavelet-ANN performed poorly across all metrics. ANN recorded a mean MAE of 0.9506 and RMSE of 1.0761 with an extremely negative R² of -39.8991, while EMD-ANN and Wavelet-ANN recorded MAE above 1.0 and RMSE above 1.1, with R² values of approximately -52.59 and -54.90 respectively. Their percentage errors were also high, with MAPE values ranging between 16.84 and 21.10 percent. These results suggest that simple feedforward ANNs and hybrid decomposition-based architectures were not well-suited to this dataset, potentially due to overfitting and lack of effective temporal structure capture.

The best model for each crop yield forecast for next 20 years shown in Figure 2. Residual diagnostics across models indicated no significant ARCH effects, implying that volatility clustering was not a primary concern in this dataset. CDVI values averaged consistently around 20.7 across models, reflecting inherent variability tied to crop characteristics rather than specific model outputs. Thus, variability indices did not differentiate strongly between approaches.

Figure 3 shows the RMSE and R² score values of all models. The model with the lowest RMSE and the highest R² is the best performing among all hybrid models. In synthesis, the ranking of models based on overall crop performance shows PLS and ETS-based hybrids as the strongest performers, followed by standalone LSTM. ARIMA achieved moderate performance, while ANN and decomposition-driven hybrids underperformed significantly. The contrast between strong linear or hybrid models and weak standalone nonlinear models highlights that capturing agricultural yield dynamics benefits from either linear dimension reduction (as in PLS) or hybrid smoothing mechanisms (as in ETS-ANN), rather than relying solely on deep or shallow neural networks. The performance of crop yield forecasting for globally used crops is shown in Table 3. The ETS-ANN model achieved highest R² whereas PLS achieved lowest R². The yield instability using CDVI of top five crops is shown in Figure 4.

The Table 4 shows the best five models of each crop yield prediction showing ETS-ANN often perform best whereas optimal model depends on crop.

5. Discussion

The study results indicate that hybrid models consistently outperform standalone statistical models. Deep learning models such as LSTM show superior performance for crops exhibiting strong nonlinear temporal dependencies. Wavelet-ANN and EMD-ANN models demonstrate robustness in handling nonstationary yield patterns, confirming the effectiveness of signal decomposition techniques. Volatility-based models reveal significant heteroscedasticity in several crops, justifying the inclusion of GARCH-family models. The findings highlight that no single model is universally optimal, reinforcing the need for a hybrid and comparative framework.

6. Conclusions

The comparative evaluation across crops demonstrates that hybrid and dimension reduction methods are consistently more effective for crop yield forecasting than standalone neural networks or classical linear models. Partial Least Squares achieved the best aggregate error performance, while ETS-ANN, ETS-LSTM, and ETS-SVM hybrids also provided highly competitive forecasts with low percentage errors. Standalone LSTM performed reasonably well and better than ARIMA in error terms, though both maintained negative R² values, suggesting limited explained variance capacity. ARIMA, while not the best model, offered staple performance with lower errors than ANN-based decomposition models, confirming its value as a robust baseline. By contrast, ANN, EMD-ANN, and Wavelet-ANN produced the weakest results, indicating that these models were not well adapted to the dataset. Overall, the study underscores that in agricultural yield forecasting, the integration of smoothing mechanisms or linear dimension reduction offers distinct advantages over raw machine learning models. Future work should investigate ensemble strategies that combine top performers such as PLS and ETS-hybrids to exploit complementary strengths. Furthermore, applying statistical significance tests like the Diebold-Mariano test would provide deeper validation of whether observed error differences are systematic. The findings reinforce that careful methodological choice is critical for developing accurate and reliable forecasting systems in the agricultural domain.