The Annals of Statistics
- Ann. Statist.
- Volume 15, Number 1 (1987), 79-98.
Regression Models for Nonstationary Categorical Time Series: Asymptotic Estimation Theory
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.
Ann. Statist., Volume 15, Number 1 (1987), 79-98.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62F12: Asymptotic properties of estimators
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