Markov Chain Approach to Forecast in the Binomial Autoregressive Models

Abstract

In this paper we consider the problem of forecasting binomial time series, modelled by the binomial autoregressive model. This paper considers proposed by Bu and McCabe (2008) and is extended to a higher order by Weib (2009). Since the binomial autoregressive model is a Markov chain,we can apply the earlier work of Bu and McCabe (2008) for integer valued autoregressive(INAR) model to the binomial autoregressive model. We will discuss how to compute the h-step-ahead forecast of the conditional probabilities of XT+h when T periods are used in fitting. Then we obtain the maximum likelihood estimator of binomial autoregressive model and use it to derive the maximum likelihood estimator of the h-step-ahead forecast of the conditional probabilities of XT+h. The methodology is illustrated by applying it to a data set previously analyzed by Weib (2009).