Study on forecasting of Indian onion export price using machine learning techniques-based hybrid models

Introduction

The global marketplace, technological innovations, and consumer demands in the onion industry continue to evolve (Raka and Ramesh, 2017) [31] . India, the world's largest onion producer, recorded an output of about 26.7 million metric tonnes in 2023-24 (Dohlman et al., 2025) [16] , and exported nearly 1.6 million metric tonnes (APEDA, 2024). However, despite strong production and exports, domestic onion prices remain highly volatile, leading to instability in farmers' incomes, consumer affordability, and export competitiveness (Debopam et al., 2021; Dhotre et al., 2025) [14,15] . Onion prices in the domestic market exhibited sharp fluctuations during 2019 and 2021, primarily due to inadequate information regarding future prices and severe supply shocks (Ghosh et al., 2022) [18] . These shocks were driven by low yields, delayed sowing, and crop losses caused by excessive rainfalls (Satish 2018; Imran et al., 2025) [33,21] . In this situation, the government imposed an onion export ban, and resorted to imports from Afghanistan, Egypt, Turkey, and Iran to stabilize the market (Biswas 2019, and Saxena et al., 2024) [6,34] . However, such interventions often result in significant financial losses for farmers (Kumar et al., 2020) [25] . Price forecasting of agricultural commodities is crucial for farmers, policymakers, and the government; however, accurate forecasting remains difficult due to unpredictable factors such as weather, market dynamics, and inadequate storage facilities (Ajmal et al., 2024) [4] . Agricultural price data are often nonstationary and nonlinear in nature (Wang et al., 2020) [45] . Traditional statistical approaches such as ARIMA, SARIMA, and GARCH have been widely applied. For instance, Agbo (2023) [2] examined export crop price volatility in Egypt using ARIMA/GARCH, Sahu (2024) [32] studied potato price and export compared ARIMA and SARIMA for onion price forecasting, confirming their short-term effectiveness. Yadav (2024) [49] further demonstrated that SARIMA outperformed other univariate models in forecasting global wheat prices. Nevertheless, while these models are valuable for linear and stationary datasets, they often fail to capture the nonlinear and highly volatile dynamics of agricultural markets. To address these limitations, machine learning (ML) and AI methods have gained prominence for their ability to capture complex patterns. Xu and Zhang (2021, 2022) [47][48] applied neural networks to commodities such as coffee, corn, cotton, soybeans, sugar, and wheat for price forecasting. Mohanty et al. (2023) [28] proposed an ML-based framework for crop price prediction, while Patil et al. (2023) [29] emphasized its role in ensuring food security. Brignoli et al. (2024) [8] applied ML to grain yield prediction futures, and Yerukala et al. (2024) [50] used neural networks for agricultural commodity forecasting. More recently, Theofilou et al. (2025) [42] demonstrated the effectiveness of ML in staple food crops. Collectively, these studies highlight the versatility of ML across diverse crops and markets, though they also caution that AI models can be prone to issues such as local minima and overfitting. To better address the nonlinearity and nonstationarity in agricultural price series, hybrid and decomposition-based approaches have received growing attention. Among these, noise-assisted decomposition methods such as EMD and EEMD have been particularly emphasized by Zhang (2003) [52] , Ince and Trafalis (2006) [22] , and Chen et al. (2012) [9] . Guo et al. (2012) [19] combined EMD with neural networks to enhance wind speed forecasting, while Abadan and Shabri (2014) [1] showed that EMD-ARIMA improved rice price forecasts. Choudhary et al. (2019) [10] demonstrated that EEMD-TDNN outperformed TDNN for potato prices. Das et al. (2020) [13] reported the superiority of EMD-SVR over standard SVR. Silva et al. (2021) [37] highlighted the effectiveness of ensemble techniques for corn and sugar, and Purohit et al. (2021) [30] applied hybrid methods to tomato, onion, and potato markets. Khan et al. (2022) [23] employed EEMD for short-term forecasts, while Zelingher and Makowski (2023) [51] demonstrated hybrid effectiveness in maize and cocoa markets. More recent studies further confirm these advancements: Shobharani et al. (2024) [36] found TDNN and hybrid approaches outperforming SARIMA for tomato and capsicum, and Mao and Soonthornphisaj (2024) [27] showed that ensemble models improved maize price prediction in Thailand. Despite these developments, onion export price forecasting remains relatively underexplored. This study addresses this gap by evaluating hybrid forecasting frameworks for Indian onion export prices with key objectives: To assess the robustness of hybrid ML models in volatile vegetable markets, and to provide actionable guidance for model selection and trade-related decision-making.

Methods and Materials 2.1 Data source

This study used monthly export price data for Indian onions (₹/Quintal) from January 2008 to December 2021, collected from the Agricultural and Processed Food Products Export Development Authority (APEDA). As shown in figure 3, data were split into training and testing sets, the first 156 observations were utilized for model building and last 12 data points were used for validation purpose. Preprocessing, modelling, and evaluation were performed using Python (v3.5), and R (v4.3.2) with packages such as forecast, t series, caret, e1071, EMD, and Rlibeemd.

Autoregressive Integrated Moving Average (ARIMA)

This model is one of the most widely used approaches for time series forecasting. It is denoted as ARIMA (p, d, q), where p represents the autoregressive order, d is the degree of differencing, and q is the moving average order, defined in equation 2.2.1. ARIMA is particularly useful for modelling non-stationary linear time series. For seasonal data, the model is extended to the Seasonal ARIMA (SARIMA), denoted as ARIMA (p, d, q)(P, D, Q)s, where (P, D, Q) are the seasonal parameters and s is the seasonal period, it is stated in equation 2.2.2 (Box et al., 1976).

Where 끫료 끫룂 is the value of the price series at time t, 끫룄 끫룂 is the disturbance term at time t which is assumed to be IID with mean zero and constant variance 끫븜 2 , the backshift operator B is defined by

The polynomials are defined as:

Where the degrees of the polynomials are p, q, in B, and P, Q for 끫롪 끫룀 respectively.

Time delay neural networks (TDNNs)

ANNs are human brain-inspired models that capture time series characteristics using data-driven, nonlinear, and nonparametric methods, unlike traditional forecasting methods. Neural networks consist of three interconnected neuron layers, where each layer receives input from the previous one and sends output to the next (Singh, 2021) [38] . Nonlinear activation functions are applied at hidden nodes to transform weighted inputs, introduce nonlinearity, and regulate output values. During training, the network learns optimal weights and biases stored in its nodes, which determine the mapping between inputs and outputs. The number of input neurons corresponds to the number of lagged values used as predictors, while hidden nodes process their weighted sums through nonlinear transformations (Li et al., 2010) [26] . Mathematically, forward propagation is expressed as:

Where p and q are the number of input layers and hidden nodes, 끫료 끫룂-1 , 끫료 끫룂-2 , 끫료 끫룂-3 ….,끫료 끫룂-끫뢺 are the input patterns, 끫뷺 끫뢬끫뢮 is the synaptic weight between the i th input neuron and j th hidden neuron, 끫뷸 끫뢮 is the weight between the j th hidden neuron and the output neuron, 끫뷺 0끫뢮 and 끫뷸 0 is the bias, 끫뢨(.) are the activation functions of hidden nodes, respectively (Ahmed, 2025) [3] .

Support Vector Regression (SVR)

SVR introduced by Vapnik (1998) [43] , extends SVM to regression tasks using a loss function. It's working process is shown in figure 1, and the basic linear SVR model is defined as:

Where 끫룈 defines the weight vector, 끫븲 denotes mapping function, and 끫뢞 is bias, these parameters are estimated by minimizing a regularized risk function:

� called 'empirical error' is estimated by Vapnik ε-insensitive loss function:

Here, both c and ε are user-determined hyper-parameters, ε defines a tolerance margin around the regression function, while c is a regularization constant balancing flatness and error tolerance (Singla et al., 2021) [39] . [11] .

Empirical mode decomposition (EMD)

EMD is a type of adaptive time series decomposition approach used for nonlinear and non-stationary time series data. The method decomposes a series into a finite set of Intrinsic Mode Functions (IMFs) and a final residue (Huang et al., 1998) [20] . Each IMF represents an oscillatory mode with unique amplitude and frequency modulation, and it must satisfy two conditions: (i) the number of extrema and zero-crossings should be nearly equal, and (ii) the mean of the envelopes defined by local maxima and minima should be zero (Sonam and Kumar, 2017) [40] . The original series can then be reconstructed as:

Steps of EMD 1. Identify all local maxima and minima of the series. The possible number of IMFs that can be extracted from a time series is approximately 끫뢲끫뢸끫뢨 2 N, Where N denotes the length of the series (Wu and Huang, 2009) [46] . While EMD effectively captures hidden oscillatory patterns in nonstationary agricultural price data, a major limitation is the mode mixing problem, where signals of different scales appear in a single IMF. This reduces the interpretability of the decomposition (Sezen, 2023) [35] .

Ensemble empirical mode decomposition (EEMD)

Wu and Huang (2009) [46] introduced EEMD as an improved version of EMD to overcome the issue of mode mixing. In EEMD, white noise is repeatedly added to the original series, decomposed with EMD, and then averaged across trials to extract the true IMFs and residue. The working process is illustrated in Figure 2, and the final decomposition is represented as:

Where ℎ 끫뢮 (끫뢸) , j=1,2…..n are the final IMFs and r(t) is the residue.

Results and Discussion

In order to predict the prices of export onion, the dataset was pre-processed, a few missing values were imputed using the mean imputation method in R with the imputeTS package to ensure accuracy and consistency. Descriptive statistics (Table 1) revealed large fluctuations, with prices ranging from ₹271.57 to ₹11,405.45 per quintal and a high coefficient of variation (72.16%), reflecting substantial instability. The time plot (Figure 3) clearly revealed the presence of trend and volatility, while the seasonal boxplot (Figure 4) confirmed seasonality, and the ACF and PACF plots (Figure 5) indicated non-stationarity. Formal statistical tests further supported these findings: Shapiro-Wilk test (p< 0.01) Rejected normality, the Ljung-Box test (p< 0.01) confirmed significant autocorrelation, the KPSS test (Table 2) Indicated non-stationarity in original series but stationarity after first differencing, and the BDS test (Table 3) Confirmed the presence of nonlinearity (p< 0.01 across all dimensions). Collectively, these results confirm the data's complexity and justify the use of advanced forecasting methods. Following the identification of nature of date series, several traditional forecasting models were applied, including ARIMA, TDNN and SVR. Their predictive performance on the test dataset is reported in Table 4. An ARIMA (1,1,1) (0,0,2) [12] model was selected as optimal based on its low AIC value, and its residuals passed diagnostic checks for white noise. However, consistent with the BDS test results, its linear structure failed to capture the dataset nonlinear dynamics. Subsequently, machine learning models (ANN and SVM) were used to address this limitation.

After conducting several iterations with different nodes, the optimal ANN architecture was determined to be (12: 6S:1L), consisting of 12 input nodes, 6 hidden nodes with Tanh activation function, and 1 output node, based on their holdout forecasting performance. The RMSE of the training set (213.03) indicated strong in-sample performance, whereas the substantially larger RMSE of the test set (1643.08) confirmed overfitting (Table 5). In contrast, SVR, tuned via 10-fold cross-validation including an RBF kernel with the hyper parameters (Cost = 1, Gamma = 0.1, Epsilon = 0.1), achieved better robustness and higher predictive accuracy than TDNN, as shown in Figures 9 and10.

To enhance prediction accuracy, hybrid models using EMD and EEMD decomposition were applied. The series was decomposed into six IMFs and one residual (Figures 67), where amplitudes decreased from IMF1 to IMF6 and the residual captured the random trend. This decomposition revealed hidden patterns, improving the forecasting performance of ARIMA, TDNN, and SVR (Das et al., 2023) [12] . Each decomposed dataset was modeled as in the single-model approach, and final fitted results are then obtained following the procedure outlined in section 2.5 and 2.6 of the methodology. The results (Table 4) indicated that the EEMD-SVR model produced forecasts closer to the test data than the other models, as illustrated in Figure 8, effectively capturing both linear and nonlinear dynamics. The predictive performance of nine models for forecasting onion export prices was evaluated using RMSE and MAPE metrics (Table 5). 6 confirm that EEMD-SVR was significantly more accurate than all other hybrids. The enhanced performance of EEMD-SVR can be attributed to the decomposition process, which isolates and identifies distinct features of price volatility, improving the forecasting process.

Conclusion

Farmers and traders can reduce losses with advance price information, which is especially important for perishable crops like tomatoes, onions, and potatoes. In this study, we forecast onion export prices using hybrid machine learning and classical models, focusing on handling both nonstationary and nonlinear data. We used decomposition techniques, EMD and EEMD, to break the series into simpler components, predicted them with ARIMA, TDNN, and SVR, and combined the results for the final forecast. EEMD improved prediction accuracy compared to EMD. Some small errors may occur due to external factors like weather. Accurate forecasts help farmers make better decisions on production and marketing, and assist the government in planning import and export policies.

Acknowledgement

AcknowledgementsI am indeed grateful to the Editors for their guidance and counsel. I am very grateful to the reviewer for valuable comments and suggestions of generously listing many useful references.

References

1. Abadan S, Shabri A. Hybrid empirical mode decomposition-ARIMA for forecasting price of rice. Applied Mathematical Sciences. 2014;8(63):3133-3143.
2. Agbo HMS. Forecasting agricultural price volatility of some export crops in Egypt using ARIMA/GARCH model. Review of Economics and Political Science. 2023;8(2):123-133.
3. Ahmed I. A machine learning approach to short-term price forecasting of agricultural crops in India. In: 2025 First International Conference on Advances in Computer Science, Electrical, Electronics, and Communication Technologies (CE2CT). IEEE; 2025 Feb. p. 325-331.
4. Ajmal S, Rohith S, Unniravisankar P, Nabay A. Price dynamics of tomato, onion and potato (TOP) in India. Asian Journal of Agricultural Extension, Economics & Sociology. 2024;42:134-143.
5. Agricultural and Processed Food Products Export Development Authority. Fresh onions: export volume in FY23-24. New Delhi: Agricultural and Processed Food Products Export Development Authority; 2024.
6. Biswas P. Explained: What is driving onion prices. Indian Express. 2019 Nov 18.
7. Box GE. Science and statistics. Journal of the American Statistical Association. 1976;71(356):791-799.
8. Brignoli PL, Varacca A, Gardebroek C, Sckokai P. Machine learning to predict grains futures prices. Agricultural Economics. 2024;55(3):479-497.
9. Chen CF, Lai M, Yeh CC. Forecasting tourism demand based on empirical mode decomposition. KnowledgeBased Systems. 2012;26:281-287.
10. Choudhary K, Jha GK, Kumar RR, Mishra DC. Agricultural commodity price analysis using ensemble empirical mode decomposition: A case study of daily potato price series. Indian Journal of Agricultural Sciences. 2019;89(5):882-886.
11. Das P. Study on machine learning techniques based hybrid model for forecasting in agriculture. 2019.
12. Das P, Jha GK, Lama A. Empirical mode decomposition based ensemble hybrid machine learning models for agricultural commodity price forecasting. Statistics Applications. 2023;99:1-??.
13. Das P, Jha GK, Lama A, Parsad R, Mishra D. Empirical mode decomposition based support vector regression for agricultural price forecasting. Indian Journal of Extension Education. 2020;56(2):7-12.
14. Debopam R, Paul RK, Panwar S. Asymmetric price volatility of onion in India. Indian Journal of Agricultural Economics. 2021;76(2):245-260.
15. Dhotre M, Nithin KN, Kolluru R, Desai S. Recurring onion and tomato crises in India: A critical analysis and future perspectives. In: Emerging Trends in Food and Agribusiness Marketing. Hershey (PA): IGI Global; 2025. p. 123-160.
16. Dohlman E, Hansen J, Chambers W, Interagency Agricultural Projections Committee. USDA agricultural projections to 2034. Washington (DC): United States Department of Agriculture; 2025.
17. GH HN. A comparative analysis of time series models for onion price forecasting: Insights for agricultural economics. Journal of Experimental Agriculture International. 2024;46(5):146-154.
18. Ghosh S, Datta D, Majumdar B, Mazumdar SP, Soumia PS, Thangasamy A. Onion price fluctuation in Indian market: Analysis and mitigation strategies. Vigyan Varta International E-Magazine of Science Enthusiasts. 2022;3(4):95-98.
19. Guo Z, Zhao W, Lu H, Wang J. Multi-step forecasting for wind speed using a modified EMD-based artificial neural network model. Renewable Energy. 2012;37(1):241-249.
20. Huang NE, Shen Z, Long SR, Wu ML, Shih HH, Zheng Q, et al. The empirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London Series A. 1998;454:909-995.
21. Imran M, Kang H, Lee SG, Kim EH, Park HM, Oh SW. Current trends and future prospects in onion production, supply, and demand in South Korea: A comprehensive review. Sustainability. 2025;17(3):1-??.
22. Ince H, Trafalis T. A hybrid model for exchange rate prediction. Decision Support Systems. 2006;42(2):1054-1062.
23. Khan DM, Ali M, Iqbal N, Khalil U, Aljohani HM, Alharthi AS, et al. Short-term prediction of COVID-19 using novel hybrid ensemble empirical mode decomposition and error trend seasonal model. Frontiers in Public Health. 2022;10:922795.
24. Kim D, Oh HS. EMD: a package for empirical mode decomposition and Hilbert spectrum. The R Journal. 2009;1(1):40-42.
25. Kumar P, Badal PS, Paul RK, Jha GK, Venkatesh P, Kingsley IT, et al. Empowering farmers through future price information: A case of price forecasting of brinjal in eastern Uttar Pradesh. Indian Journal of Economics and Development. 2020;16(4):479-488.
26. Li G, Xu S, Li G. Short-term price forecasting for agroproducts using artificial neural networks. Agriculture and Agricultural Science Procedia. 2010;3(1):278-287.
27. Mao S, Soonthornphisaj N. Thailand's maize prices forecasting using ensemble technique. ASEAN Journal of Scientific and Technological Reports. 2024;27(4):e252279.
28. Mohanty MK, Thakurta PKG, Kar S. Agricultural commodity price prediction model: a machine learning framework. Neural Computing and Applications. 2023;35(20):15109-15128.
29. Patil A, Shah D, Shah A, Kotecha R. Forecasting prices of agricultural commodities using machine learning for global food security: towards sustainable development goal 2. International Journal of Engineering Trends and Technology. 2023;71:277-291.
30. Purohit SK, Panigrahi S, Sethy PK, Behera SK. Time series forecasting of price of agricultural products using hybrid methods. Applied Artificial Intelligence. 2021;35(15):1388-1406.
31. Raka S, Ramesh C. Understanding the recurring onion price shocks: revelations from production-trade-price linkages. Policy Paper -National Centre for Agricultural Economics and Policy Research. 2017;6(33):56-59.
32. Sahu PK, Das M, Sarkar B, VS A, Dey S, Narasimhaiah L, et al. Potato production in India: a critical appraisal on sustainability, forecasting, price and export behaviour. Potato Research. 2024;67(4):1209-1245.
33. Satish DP. Onion price hits rock bottom, sells at Rs 1 per kilo in Karnataka. News18. 2018 Nov 21.
34. Saxena R, Birthal PS, Agrawal RC, Sharma P, Paul BS, Pant DK, et al. From local to global opportunities to accelerate agricultural exports from India. New Delhi; 2024.
35. Sezen C. Pan evaporation forecasting using empirical and ensemble empirical mode decomposition (EEMD) based data-driven models in the Euphrates sub-basin, Turkey. Earth Science Informatics. 2023;16(4):30773095.
36. Shobharani HM, Gupta AK, Kumar S, Tripathi G. Machine learning and hybrid model building mechanism for forecasting agricultural market behaviour: a case study of vegetable crops. Indian Journal of Economics and Development. 2024;20:303316.
37. Silva RF, Barreira BL, Cugnasca CE. Prediction of corn and sugar prices using machine learning, econometrics, and ensemble models. Engineering Proceedings. 2021;9:31.
38. Singh A. Comparison of artificial neural networks and statistical methods for forecasting prices of different edible oils in Indian markets. International Research Journal of Modernization in Engineering Technology and Science. 2021;3(10):1044-1050.
39. Singla S, Paul RK, Shekhar S. Modelling price volatility in onion using wavelet-based hybrid models. Indian Journal of Economics and Development. 2021;17(2):256-265.
40. Sonam M, Kumar A. Empirical mode decomposition: theory and applications. International Journal of Electronic and Electrical Engineering. 2017;7(8):873878.
41. Sunil J, Sindhu D. Growth status and ARIMA model forecast of area, production of wheat crop in India. Journal of Scientific Research and Reports. 2020;26(5):117-125.
42. Theofilou A, Nastis SA, Michailidis A, Bournaris T, Mattas K. Predicting prices of staple crops using machine learning: a systematic review of studies on wheat, corn, and rice. Sustainability. 2025;17(12):5456.
43. Vapnik V. The support vector method of function estimation. In: Nonlinear modeling: advanced blackbox techniques. 1998. p. 55-85.
44. Wang G, Xu S, Chen Z, Li Y. A hybrid model integrating variational mode decomposition and intelligent optimization for vegetable price prediction. Agriculture. 2025;15(9):919.
45. Wang L, Feng J, Sui X, Chu X, Mu W. Agricultural product price forecasting methods: research advances and trend. British Food Journal. 2020;118(5):11291145.
46. Wu Z, Huang NE. Ensemble empirical mode decomposition: a noise-assisted data analysis method. Advances in Adaptive Data Analysis. 2009;1(1):1-41.
47. Xu X, Zhang Y. Corn cash price forecasting with neural networks. Computers and Electronics in Agriculture. 2021;184:106120.
48. Xu X, Zhang Y. Commodity price forecasting via neural networks for coffee, corn, cotton, oats, soybeans, soybean oil, sugar, and wheat. Intelligent Systems in Accounting, Finance and Management. 2022;29(3):169-181.
49. Yadav A. A comparative study of time series, machine learning, and deep learning models for forecasting global price of wheat. In: Operations Research Forum. Cham: Springer International Publishing; 2024 Nov. Vol 5(4):113.
50. Yerukala S, Madala P, Battula V, Enduri MK, Tokala S, Bisiringi NP. Estimating future prices of key agricultural commodities using machine learning models. In: 2024 Beyond Technology Summit on Informatics International Conference (BTS-I2C). IEEE; 2024 Dec. p. 572-576.
51. Zelingher R, Makowski D. Investigating and forecasting the impact of crop production shocks on global commodity prices. Environmental Research Letters. 2024;19(1):014026.
52. Zhang GP. Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing. 2003;50(2):159-175.
53. Zhang N, An Q, Zhang S, Ma H. Price prediction for fresh agricultural products based on boosting ensemble algorithm. Mathematics. 2025;13(1):71.