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The impact of unsuspected serial correlations on model selection in linear regression

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  • Hurvich, Clifford M.
  • Tsai, Chih-Ling

Abstract

We obtain the asymptotic distributions of the linear regression models selected by the Akaike Information Criterion (AIC) and the Schwarz Information Criterion (BIC), in the presence of unsuspected serial correlations. We assume that the models are fitted by ordinary least squares to a data set observed at equally spaced intervals of time, and that the errors are a stationary Gaussian process. We also assume that the true model is of finite dimension, and that the set of candidate models is held fixed as the sample size increases. We will show that, for AIC, the asymptotic probability of underfitting is zero, regardless of the error correlation structure, while the asymptotic probability of overfitting depends on the error correlations. Furthermore, we will show that BIC is consistent. Our results generalize those of Nishii (1984), who assumed an i.i.d. Gaussian error structure. Finally, we will present the results of a simulation study, which provides support for the applicability in moderate sample sizes of our asymptotic theorems.

Suggested Citation

  • Hurvich, Clifford M. & Tsai, Chih-Ling, 1996. "The impact of unsuspected serial correlations on model selection in linear regression," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 115-126, April.
    • Handle: RePEc:eee:stapro:v:27:y:1996:i:2:p:115-126
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    Cited by:

    1. Burcu Gurcihan Yunculer & Gonul Sengul & Arzu Yavuz, 2014. "A Quest for Leading Indicators of the Turkish Unemployment Rate," Central Bank Review, Research and Monetary Policy Department, Central Bank of the Republic of Turkey, vol. 14(1), pages 23-45.

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    Keywords

    AIC BIC;

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