The Annals of Statistics

Regression Models for Nonstationary Categorical Time Series: Asymptotic Estimation Theory

Heinz Kaufmann

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350254

Digital Object Identifier
doi:10.1214/aos/1176350254

Mathematical Reviews number (MathSciNet)
MR885725

Zentralblatt MATH identifier
0614.62111

JSTOR
links.jstor.org

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

Keywords
Time series categorical data nonstationary Markov chains asymptotic estimation theory

Citation

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. https://projecteuclid.org/euclid.aos/1176350254


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