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Quasi-Likelihood Regression Models for Markov Chains

Wolfgang Wefelmeyer
Lecture Notes-Monograph Series
Vol. 32, Selected Proceedings of the Symposium on Estimating Functions (1997), pp. 149-173
Stable URL: http://www.jstor.org/stable/4356015
Page Count: 25
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Quasi-Likelihood Regression Models for Markov Chains
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Abstract

We consider regression models in which covariates and responses jointly form a higher order Markov chain. A quasi-likelihood model specifies parametric models for the conditional means and variances of the responses given the past observations. A simple estimator for the parameter is the maximum quasi-likelihood estimator. We show that it does not use the information in the model for the conditional variances, and construct an efficient estimating function which involves estimators for the third and fourth centered conditional moments of the responses. In many applications one assumes that the innovations are not arbitrary martingale increments but independently and identically distributed. We determine how much additional information about the parameter such an assumption contains. To make the exposition more readable, we first treat the case in which only the conditional mean is specified.

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