Regime-Adaptive ARIMA–GARCH Framework under Structural Break: Evidence from the S&P 500 Index
Abstract
Financial time series forecasting faces challenges from structural instability caused by macroeconomic shocks. The hybrid Autoregressive Integrated Moving Average-Generalized Autoregressive Conditional heteroskedasticity models (ARIMA-GARCH models) can capture temporal dependencies and volatility in financial time series but tend to produce inaccurate forecasts as they assume constant model parameters across structural breaks in the series. This study develops a forecasting framework that incorporates structural break parameters into the ARIMA-GARCH model. The study uses monthly closing price of S&P 500 index from January 2001 to December 2017. The Bai-Perron test is used to identify the structural breaks in the time series, followed by modelling the ARIMA mean and GARCH variance of the series in each regime. The structural break in early 2009 is identified as a transition from a moving-average process in the pre-crisis period to a random walk process in the post-crisis period. Simulations studies indicate that the proposed framework significantly reduces distortions. The Mean Absolute Percentage Error (MAPE) in the forecast reduces from 59.8% in the full-sample ARIMA-GARCH model to 13.0% in the regime-adaptive model. The regime-adaptive model developed in this study offers a better tool for forecasting the S&P 500 index, particularly during periods of high volatility.
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References
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