## The Annals of Statistics

### Order Selection in Nonstationary Autoregressive Models

Ruey S. Tsay

#### 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

#### 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