346 – Time Series: Stationarity, Non-Stationarity, Cointegration, ARCH Models, and GARCH Models
Autoregressive Conditional Heteroscedastic Hidden Markov Model
Yi Zhang
Missouri University of Science and Technology
With the rapid development of sensors and other data-gathering devices, high-frequency time series of count data have become common. Such series commonly exhibit conditional dependence of the parameters of the data generating process (DGP) to past values of the counts and parameter values. The Autoregressive Conditional Poisson (ACP) formulation is one model developed to describe the underlying data generating mechanism of such processes. In ACP Models, the mean of the Poisson process is assumed to be a linear function of past means and past counts through a GARCH type model. In this formulation, it is assumed that the parameters of the model that connects the conditional mean to past values remain constant over time. One generalization is to accommodate seasonal variations in one or more of these parameters, but in some empirical processes, the changes in the parameters may not occur systematically but according to a latent process. The proposed model addresses such a scenario where the Poisson intensity is modeled using an ARCH type formulation with select parameters taking different values based on the state defined by a hidden Markov chain. The application of the proposed model is illustrated using a synthetic and a real-life data set.