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.
Keywords
Autoregressive modelMathematicsSTAR modelModel selectionSeries (stratigraphy)Asymptotic distributionApplied mathematicsSelection (genetic algorithm)SETAREconometricsAutoregressive integrated moving averageLimitingStationary processTime seriesStatisticsComputer scienceArtificial intelligenceEstimator
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Publication Info
- Year
- 1984
- Type
- article
- Volume
- 12
- Issue
- 4
- Citations
- 97
- Access
- Closed
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Cite This
Ruey S. Tsay
(1984).
Order Selection in Nonstationary Autoregressive Models.
The Annals of Statistics
, 12
(4)
.
https://doi.org/10.1214/aos/1176346801
Identifiers
- DOI
- 10.1214/aos/1176346801