The Annals of Statistics

Regression Models for Nonstationary Categorical Time Series: Asymptotic Estimation Theory

Heinz Kaufmann

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For the analysis of nonstationary categorical time series, a parsimonious and flexible class of models is proposed. These models are generalizations of regression models for stochastically independent categorical observations. Consistency, asymptotic normality and efficiency of the maximum likelihood estimator are shown under weak and easily verifiable requirements. Some models for binary time series are discussed in detail. To demonstrate asymptotic properties, a theorem is given addressing maximum likelihood estimation for general stochastic processes. Then it is shown that the assumptions of this theorem are consequences of the requirements for categorical time series. For this proof some lemmas are used which may be of interest in similar cases.

Article information

Ann. Statist., Volume 15, Number 1 (1987), 79-98.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62F12: Asymptotic properties of estimators

Time series categorical data nonstationary Markov chains asymptotic estimation theory


Kaufmann, Heinz. Regression Models for Nonstationary Categorical Time Series: Asymptotic Estimation Theory. Ann. Statist. 15 (1987), no. 1, 79--98. doi:10.1214/aos/1176350254.

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