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.

翻译：持续时间依赖的马尔可夫转换(DDMS)模型中最关键的超参数之一是隐状态的持续时间。由于目前尚无估计该持续时间或检验给定持续时间是否适用于特定数据集的标准化流程，研究人员必须通过启发式方法论证人为选定的持续时间。这通常是一项艰巨的任务，且极有可能成为建模过程中最棘手的环节，不仅易受到质疑，最终还会阻碍DDMS模型的推广应用。本文针对以预测为目标的场景，提出并检验了一种缓解DDMS模型持续时间选择问题的方法论。其核心思想是在计算转移概率时采用参数化链接替代传统的固定链接。这使得模型更具灵活性，任何潜在的持续时间选择偏差(即设定错误)均可通过链接中的参数得到补偿，从而获得与真实值极为接近的似然函数和转移概率，同时提升设定错误情形下的预测精度。我们通过蒙特卡洛模拟和实际数据应用对提出的方法进行了评估。结果表明，无论在设定正确还是设定错误的持续时间条件下，参数化链接模型在样本内估计和样本外预测两方面均优于基准逻辑模型。