## Order selection in nonstationary autoregressive models.(English)Zbl 0554.62075

In E. J. Hannan [ibid. 8, 1071-1081 (1980; Zbl 0451.62068)], 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 R. Shibata [Biometrika 63, 117-126 (1976; Zbl 0358.62048)] for the stationary autoregressive models continues to hold.

### MSC:

 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60F15 Strong limit theorems

### Citations:

Zbl 0451.62068; Zbl 0358.62048
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