Chan, K. S.; Ledolter, Johannes Monte Carlo EM estimation for time series models involving counts. (English) Zbl 0819.62069 J. Am. Stat. Assoc. 90, No. 429, 242-252 (1995). Summary: The observations in parameter-driven models for time series of counts are generated from latent unobservable processes that characterize the correlation structure. These models result in very complex likelihoods, and even the EM algorithm, which is usually well suited for problems of this type, involves high-dimensional integration. We discuss a Monte Carlo EM (MCEM) algorithm that uses a Markov chain sampling technique in the calculation of the expectation in the \(E\) step of the EM algorithm. We propose a stopping criterion for the algorithm and provide rules for selecting the appropriate Monte Carlo sample size. We show that under suitable regularity conditions, an MCEM algorithm will, with high probability, get close to a maximizer of the likelihood of the observed data. We also discuss the asymptotic efficiency of the procedure. We illustrate our Monte Carlo estimation method on a time series involving small counts: the polio incidence time series previously analyzed by S. L. Zeger [Biometrika 75, No. 4, 621-629 (1988; Zbl 0653.62064)]. Cited in 1 ReviewCited in 82 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F12 Asymptotic properties of parametric estimators 62P10 Applications of statistics to biology and medical sciences; meta analysis 65C99 Probabilistic methods, stochastic differential equations Keywords:Monte Carlo EM algorithm; generalized regression model; parameter-driven models; time series of counts; latent unobservable processes; correlation structure; Markov chain sampling; EM algorithm; stopping criterion; MCEM algorithm; asymptotic efficiency; Monte Carlo estimation; polio incidence time series Citations:Zbl 0653.62064 PDFBibTeX XMLCite \textit{K. S. Chan} and \textit{J. Ledolter}, J. Am. Stat. Assoc. 90, No. 429, 242--252 (1995; Zbl 0819.62069) Full Text: DOI