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. This is typically a difficult task and is likely the most delicate point of the modeling procedure, allowing for criticism and ultimately hindering the use of DDMS models. In this paper, we propose and examine a methodology that mitigates the choice of duration in DDMS models when forecasting is the goal. The idea is to use a parametric link instead of the usual fixed link when calculating transition probabilities. As a result, the model becomes more flexible and any potentially incorrect duration choice (i.e., misspecification) is compensated by the parameter in the link, yielding a likelihood and transition probabilities very close to the true ones while, at the same time, improving forecasting accuracy under misspecification. We evaluate the proposed approach in Monte Carlo simulations and using real data applications. Results indicate that the parametric link model outperforms the benchmark logit model, both in terms of in-sample estimation and out-of-sample forecasting, for both well-specified and misspecified duration values.