Markov Chain Approach to Forecast in the Binomial Autoregressive Models

Title & Authors
Markov Chain Approach to Forecast in the Binomial Autoregressive Models
Kim, Hee-Young; Park, You-Sung;

Abstract
In this paper we consider the problem of forecasting binomial time series, modelled by the binomial autoregressive model. This paper considers proposed by McKenzie (1985) and is extended to a higher order by $\small{Wei{\ss}}$(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 $\small{X_{T+h}}$ 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 $\small{X_{T+h}}$. The methodology is illustrated by applying it to a data set previously analyzed by $\small{Wei{\ss}}$(2009).
Keywords
Binomial thinning;binomial AR(p) model;Markov chain;
Language
English
Cited by
1.
Parameter estimation for binomial AR(1) models with applications in finance and industry, Statistical Papers, 2013, 54, 3, 563
2.
Binomial AR(1) processes: moments, cumulants, and estimation, Statistics, 2013, 47, 3, 494
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