Parameter-driven count time series models / Nawwal Ahmad Bukhari - Nawwal , Ahmad Bukhari (2018)
Time series data involving counts are commonly encountered in many different fields including insurance industry, economics, medicine, communications, epidemiology, hydrology and meteorology. In this study, a parameter-driven count time series model with three different distributions that are Poisson, zero-inflated Poisson and negative binomial was developed. A key property of our model is that the distributions of the observed count data are independent, conditional on the latent process, although the observations are correlated marginally. The first part of the study derives the explicit solutions of the moment properties (mean, variance, skewness and kurtosis) of the distributions together with their respective autocovariance and autocorrelation functions, up to the ith order. The empirical study shows that the derivation fits the theoretical results of an autocorrelation function. The estimation of parameter is in the second part of this study. Since the proposed model is non-linear and non-Gaussian, Monte Carlo Expectation Maximization (MCEM) algorithm with the aid of particle filtering and particle smoothing methods are applied to approximate the integrals in the E-step of the algorithm. The proposed model are illustrated with simulated data and an application on Malaysia dengue data. Simulation shows that MCEM algorithm and particle method are useful for the parameter estimation of the Poisson model. In addition, Poisson model fits better in terms of Akaike information criterion (AIC) and log-likelihood when compared with several models including model from Yang et al. (2015).