Model selection, estimation and forecasting in INAR(p) models: A likelihood-based Markov Chain approach

This paper considers model selection, estimation and forecasting for a class of integer autoregressive models suitable for use when analysing time series count data. Any number of lags may be entertained, and estimation may be performed by likelihood methods. Model selection is enhanced by the use of new residual processes that are defined for each of the p + 1 unobserved components of the model. Forecasts are produced by treating the model as a Markov Chain, and estimation error is accounted for by providing confidence intervals for the probabilities of each member of the support of the count data variable. Confidence intervals are also available for more complicated event forecasts such as functions of the cumulative distribution function, e.g., for probabilities that the future count will exceed a given threshold. A data set of Australian counts on medical injuries is analysed in detail.