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

Markov Chain Approach to Forecast in the Binomial Autoregressive Models

“…Since the binomial AR(p) model can be regarded as a Markov chain, we applied the method introduced by Bu and McCabe (2008) to the binomial AR(p) model. We derived the h-step-ahead forecasts of conditional probability distribution using a Markov chin representation of the model, and obtained the MLE of those forecast mass function.…”

“…Subsection 3.2 deals real situation of unknown parameters, so how to compute the likelihood function of binomial AR(p) model and derive the asymptotic distribution of the MLE of the h-step-ahead forecast of the conditional probabilities. Our approach is based on Bu and McCabe (2008) in INAR(p) model.…”

“…There are numerous efforts to forecast integer valued time series model using a thinning operation to resolve theses problems and to produce coherent forecasting: see Freeland and McCabe (2004) and Jung and Tremayne (2006) and Park (2006a,b, 2010) and Bu and McCabe (2008). Of theses articles, Bu and McCabe (2008) produced forecasting in INAR(p) model by treating the model as a Markov chain.…”

“…In this paper, we apply Bu and McCabe (2008)'s idea to the binomial AR(p) model to build confidence intervals for the probabilities of all possible values taken the process in the future, since the binomial AR(p) model can be viewed as a Markov chain. This paper is organized as follows.…”

“…This paper considers proposed by McKenzie (1985) and is extended to a higher order by Weiß (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 X T +h when T periods are used in fitting.…”