Comparative evaluation of ARIMA and ETS models for short-term wind speed forecasting across twelve meteorological stations in Pakistan using the expanding-window method

Abstract

This article presents a statistical forecasting framework for wind speed using two well-known classical forecasting models, the autoregressive integrated moving average (ARIMA) and the exponential smoothing state space (ETS) models with the naïve model as a benchmark for comparison. Twelve meteorological stations across Pakistan were selected based on data availability and analyzed using a comprehensive and rigorous expanding-window data-splitting method. The expanding window method iteratively extends the training data over ten successive splits, with each split used to generate seven-day-ahead wind speed predictions. This approach allows the forecasting performance of the models to be evaluated over multiple forecast origins while progressively incorporating newly available observations into the training data. Root mean square error (RMSE) and mean absolute percentage error (MAPE) were used to examine the predictive behavior of all models and to evaluate their consistency and responsiveness over time. Model comparisons were further assessed by the Diebold-Mariano (DM) test on forecast errors for each model. The ARIMA model performed better (based on RMSE) for short-term wind speed forecasting at seven stations in Pakistan while the ETS model performed better at two stations and performed equally at three stations covered by this study. The DM test also supports the RMSE- and MAPE-based results in favor of the ARIMA model. The findings demonstrate the generally stronger performance of the ARIMA model.