Combining Volatility Forecasts of Duration-Dependent Markov-Switching Models

Duration-dependent Markov-switching (DDMS) models require a user-specified duration hyperparameter, for which there is currently no established procedure for estimation or testing. As a result, an ad-hoc duration choice must be heuristically justified. This paper proposes a methodology for handling duration selection in DDMS models, with a focus on volatility forecasting. The main novelty lies in generating forecasts through model combination techniques. The idea is that the combined forecasts will be more robust to misspecification in selecting the duration structure, thus yielding more accurate forecasts. Additionally, the paper contributes to the literature by evaluating the out-of-sample volatility forecasting performance of DDMS models compared to benchmark conditional volatility models. Empirical analysis involves returns from three distinct asset classes: a cryptocurrency, a stock market index, and a foreign currency exchange rate. Various volatility proxies and robust loss functions are incorporated into our analysis. The results indicate that combined forecasts outperform individual models and, in some cases, are more accurate than GARCH and MS-GARCH models. Furthermore, models with fixed duration typically underperform relative to the simple GARCH model, often resulting in test rejections.