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.
SWITCHING REGIME INTEGER AUTOREGRESSIONS
Rossi E.;
2025-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
