A comparative study of interval forecasting using GARCH models under symmetric and asymmetric distributional assumptions

Abstract: Interval forecasting provides decision-makers with a range of possible future values, along with associated probabilities, which allows for a more informed decision-making process. Although GARCH models under different distributional assumptions are commonly compared for their volatility forecasting performance, their performance in interval forecasting is rarely discussed. This study aims to fill this gap by comparing the interval forecasting accuracy of GARCH models under symmetric and asymmetric distributions. SGARCH, EGARCH, and GJR-GARCH models under normal, student-t, GED distributions, and their skewed extensions are applied for one-day-ahead rolling interval forecasting on five major European and American stock indices: S&P 500, FTSE 100, CAC 40, DAX 30 and AEX. The average Winkler score (AWS) is used to measure the accuracy of interval forecasting. The conclusions of this study can be summarised as follows: In pairwise comparisons, the GARCH models under asymmetric distributional assumptions have better interval forecasting accuracy than the GARCH models under symmetric distributional assumptions. In comparisons among GARCH-type models, GJR-GARCH has better interval forecasting accuracy than SGARCH and EGARCH, while SGARCH and EGARCH exhibit similar interval forecasting performance.

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