Estimation of a Digitised Gaussian ARMA model by Monte Carlo Expectation Maximisation

Abstract Dependence modelling of integer-valued stationary time series has gained considerable interest. A generalisation of the ARMA model has been previously provided using the binomial operator and its estimation carried out using Markov Chain Monte Carlo methods. There are also various models that make use of a latent process. The time series is considered now as a digitised version of a Gaussian ARMA process, which is equivalent to assuming a Gaussian copula with ARMA dependence. Naturally this becomes an incomplete data problem and an EM algorithm can be used for maximum likelihood estimation. Due to the complexity of the conditional distribution given the observed data, a Monte Carlo E-step is implemented. Details of the MCEM algorithm are provided and standard errors of the parameter estimates are considered. Examples with real and simulated data are provided.