Mitigating the choice of the duration in DDMS models through a parametric link

One of the most important hyper-parameters in duration-dependent Markov-switching (DDMS) models is the duration of the hidden states. Because there is currently no procedure for estimating this duration or testing whether a given duration is appropriate for a given data set, an ad hoc duration choice must be heuristically justified. In this paper, we propose and examine a methodology that mitigates the choice of duration in DDMS models when forecasting is the goal. The novelty of this paper is the use of the asymmetric Aranda-Ordaz parametric link function to model transition probabilities in DDMS models, instead of the commonly applied logit link. The idea behind this approach is that any incorrect duration choice is compensated for by the parameter in the link, increasing model flexibility. Two Monte Carlo simulations, based on classical applications of DDMS models, are employed to evaluate the methodology. In addition, an empirical investigation is carried out to forecast the volatility of the S&P500, which showcases the capabilities of the proposed model.