Volume 15, Issue 6 · IJARST · ISSN 2319-1783 / 2320-1126

Seasonal Modeling and Forecasting of California Milk Production: A Comparative Evaluation of ARIMA, SARIMA, ARIMAX, and SARIMAX Models.

Seasonal Modeling and Forecasting of California Milk Production: A Comparative Evaluation of ARIMA, SARIMA, ARIMAX, and SARIMAX Models. is an open-access, peer-reviewed research paper by Kajol Bala, Chayan Halder, published in Volume 15, Issue 6 of the International Journal of Advanced Research in Science and Technology (IJARST), a UGC-approved journal (Print ISSN 2319-1783, Online ISSN 2320-1126).

Author

Kajol Bala, Chayan Halder

Abstract

Reliable forecasts of agricultural commodity production underpin planning decisions across supply chains, from farm-level resource allocation to regional policy. This study examines monthly California milk production from 1995 to 2013 to identify the most suitable time series model for forecasting. The data exhibit a clear long-term upward trend alongside strong annual seasonal fluctuation. After applying both regular and seasonal differencing, ACF and PACF patterns were examined to guide model identification, and four non-seasonal ARIMA models were built, three specified manually and one selected automatically via auto.arima(). The automated ARIMA (4,1,1) model achieved the best AIC and BIC values, but its residuals failed the Ljung-Box test, indicating that important structure, most likely seasonality, remained unaccounted for. This led to the development of SARIMA, ARIMAX, and SARIMAX models. Evaluated on a 12-month holdout period, SARIMA clearly outperformed the alternatives (RMSE = 0.053, MAE = 0.045, MAPE = 1.30%), far surpassing the base ARIMA model (RMSE = 0.158, MAPE ≈ 3.78%), while the exogenous-regressor variants offered little additional benefit. The findings demonstrate that a model favored by AIC can still be structurally inadequate, and that overlooking seasonality in agricultural time series leads to substantially biased forecasts.

DOI: https://doi.org/10.62226/ijarst20262708

Data and Code Availability: The dataset and analysis code used in this study are publicly available at the following locations:  California Dairy Production data: https://github.com/petershahlevlnow/DataAnalytics/blob/master/CADairyProduction.csv

The following R code was used for data preprocessing and model building. Code Download Link: https://drive.google.com/file/d/1Tidtc0UEA28CVsTA8kpxxohC0DD9Ue9H/view?usp=sharing

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DOI

https://doi.org/10.62226/ijarst20262708

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How do you cite this paper?

Kajol Bala, Chayan Halder — “Seasonal Modeling and Forecasting of California Milk Production: A Comparative Evaluation of ARIMA, SARIMA, ARIMAX, and SARIMAX Models..” International Journal of Advanced Research in Science and Technology (IJARST), Volume 15, Issue 6. DOI: https://doi.org/10.62226/ijarst20262708.

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