The Annals of Statistics

Model Selection Under Nonstationarity: Autoregressive Models and Stochastic Linear Regression Models

B. M. Potscher

Full-text: Open access

Abstract

We give sufficient conditions for strong consistency of estimators for the order of general nonstationary autoregressive models based on the minimization of an information criterion a la Akaike's (1969) AIC. The case of a time-dependent error variance is also covered by the analysis. Furthermore, the more general case of regressor selection in stochastic regression models is treated.

Article information

Source
Ann. Statist., Volume 17, Number 3 (1989), 1257-1274.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347267

Digital Object Identifier
doi:10.1214/aos/1176347267

Mathematical Reviews number (MathSciNet)
MR1015149

Zentralblatt MATH identifier
0683.62049

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62J05: Linear regression 60G10: Stationary processes 62F12: Asymptotic properties of estimators 93E12: System identification

Keywords
Model selection order estimation selection of regressors strong consistency autoregression nonstationarity nonergodic models information criteria

Citation

Potscher, B. M. Model Selection Under Nonstationarity: Autoregressive Models and Stochastic Linear Regression Models. Ann. Statist. 17 (1989), no. 3, 1257--1274. doi:10.1214/aos/1176347267. https://projecteuclid.org/euclid.aos/1176347267


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