SWITCHING REGIME INTEGER AUTOREGRESSIONS
将整数自回归模型与隐马尔可夫结构结合，提出HMM-INAR框架，推导了遍历性、渐近分布和EM算法，并应用于标普500ETF交易次数数据，相比其他计数模型拟合更好且保留经济解释。
Time series of counts often display complex dynamic and distributional characteristics. For this reason, we develop a flexible framework combining the integer-valued autoregressive (INAR) model with a latent Markov structure, leading to the hidden Markov model-INAR (HMM-INAR). First, we illustrate conditions for the existence of an ergodic and stationary solution and derive closed-form expressions for the autocorrelation function and its components. Second, we show consistency and asymptotic normality of the conditional maximum likelihood estimator. Third, we derive an efficient expectation–maximization algorithm with steps available in closed form which allows for fast computation of the estimator. Fourth, we provide an empirical illustration and estimate the HMM-INAR on the number of trades of the Standard & Poor’s Depositary Receipts S&P 500 Exchange-Traded Fund Trust. The combination of the latent HMM structure with a simple INAR $(1)$ formulation not only provides better fit compared to alternative specifications for count data, but it also preserves the economic interpretation of the results.