Enhancing inflation forecasting across short- and long-term horizons in IRAN: a hybrid approach integrating machine learning, deep learning, ARIMA, and optimized nonlinear grey Bernoulli model

Inflation forecasting remains a critical challenge in economic research and policymaking, requiring accurate and adaptive models to capture both short-term volatility and long-term trends. This study proposes a hybrid forecasting framework integrating Machine Learning (ML), Deep Learning, ARIMA, and the Nonlinear Grey Bernoulli Model (NGBM) optimized using the Imperialist Competitive Algorithm (ICA) to enhance inflation prediction accuracy across different time horizons. The research employs Bidirectional Long Short-Term Memory (BILSTM), Gradient Boosting Machines (GBM), Elastic-Net regression, and ARIMA to model inflation by all datasets for the long-term horizon (ten-step-ahead), while NGBM, optimized via ICA, Krill Herd (KH), and Political Optimization Algorithm (POA), is used for short-term forecasting (three-step-ahead) by recent data. A k-fold cross-validation technique ensures robustness and model generalizability. Empirical validation of Iran’s inflation data from 1937 to 2020 for the long-term and 2010 to 2020 for short-term forecasts reveals that BILSTM achieves the lowest RMSE (0.0532), while ICA-optimized NGBM (RMSE: 0.118) outperforms alternative short-term models. Additionally, the study reveals notable differences between forecasting with all datasets and recent data to predict ten-step-ahead and three-step-ahead. We conducted a Wilcoxon signed-rank test to determine whether the differences in predictive accuracy between the short-term (NGBM-ICA) and long-term (BILSTM) forecasting models are statistically significant. This analysis confirms that forecasting short-term inflation trends using recent data fundamentally differs from long-term forecasting based on the complete historical data set. This highlights the importance of selecting an appropriate modeling approach based on forecasting objectives. The findings offer actionable insights for policymakers and financial analysts.