The Annals of Statistics

Order Selection in Nonstationary Autoregressive Models

Ruey S. Tsay

Full-text: Open access

Abstract

In Hannan (1980), some limiting properties of the order selection criteria, AIC, BIC, and $\phi(p, q)$ for modeling stationary time series were derived. In this paper, we generalize these properties to the case in which the underlying process follows a nonstationary autoregressive model. We show that BIC and $\phi(p, 0)$ are weakly consistent. For the AIC, we prove that the asymptotic distribution given by Shibata (1976) for the stationary autoregressive models continues to hold.

Article information

Source
Ann. Statist., Volume 12, Number 4 (1984), 1425-1433.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346801

Digital Object Identifier
doi:10.1214/aos/1176346801

Mathematical Reviews number (MathSciNet)
MR760697

Zentralblatt MATH identifier
0554.62075

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60F15: Strong theorems

Keywords
AIC autoregressive model BIC model identification regression

Citation

Tsay, Ruey S. Order Selection in Nonstationary Autoregressive Models. Ann. Statist. 12 (1984), no. 4, 1425--1433. doi:10.1214/aos/1176346801. https://projecteuclid.org/euclid.aos/1176346801


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