This paper introduces a Duration Hidden Markov Model to model bull and bear market regime switches in the stock market; the duration of each state of the Markov Chain is a random variable that depends on a set of exogenous variables. The model not only allows the endogenous determination of the different regimes and but also estimates the effect of the explanatory variables on the regimes' durations. The model is estimated here on NYSE returns using the short-term interest rate and the interest rate spread as exogenous variables. The bull market regime is assigned to the identified state with the higher mean and lower variance; bull market duration is found to be negatively dependent on short-term interest rates and positively on the interest rate spread, while bear market duration depends positively the short-term interest rate and negatively on the interest rate spread.

本文引入了一种持续时间隐马尔可夫模型来模拟股票市场的牛市和熊市机制转换;马尔可夫链的每个状态的持续时间是一个随机变量，它依赖于一组外生变量。该模型不仅允许不同体系的内生决定，而且还估计解释变量对体系持续时间的影响。该模型是在纽约证券交易所收益估计使用短期利率和利率利差作为外生变量。牛市机制被分配到具有较高均值和较低方差的确定状态;牛市持续时间与短期利率呈负相关，与利率息差呈正相关;熊市持续时间与短期利率呈正相关，与利率息差呈负相关。