MCMC for integer valued ARMA processes

Neal, Peter John and Subba Rao, Tata (2007) MCMC for integer valued ARMA processes. Journal of Time Series Analysis, 28 (1). pp. 92-110. ISSN 0143-9782

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Abstract

The classical statistical inference for integer-valued time-series has primarily been restricted to the integer-valued autoregressive (INAR) process. Markov chain Monte Carlo (MCMC) methods have been shown to be a useful tool in many branches of statistics and is particularly well suited to integer-valued time-series where statistical inference is greatly assisted by data augmentation. Thus in this article, we outline an efficient MCMC algorithm for a wide class of integer-valued autoregressive moving-average (INARMA) processes. Furthermore, we consider noise corrupted integer-valued processes and also models with change points. Finally, in order to assess the MCMC algorithms inferential and predictive capabilities we use a range of simulated and real data sets.