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Prediction Errors In Nonstationary Autoregressions Of Infinite Order

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  • Ing, Ching-Kang
  • Sin, Chor-yiu
  • Yu, Shu-Hui

Abstract

Assume that observations are generated from nonstationary autoregressive (AR) processes of infinite order. We adopt a finite-order approximation model to predict future observations and obtain an asymptotic expression for the mean-squared prediction error (MSPE) of the least squares predictor. This expression provides the first exact assessment of the impacts of nonstationarity, model complexity, and model misspecification on the corresponding MSPE. It not only provides a deeper understanding of the least squares predictors in nonstationary time series, but also forms the theoretical foundation for a companion paper by the same authors, which obtains asymptotically efficient order selection in nonstationary AR processes of possibly infinite order.

Suggested Citation

  • Ing, Ching-Kang & Sin, Chor-yiu & Yu, Shu-Hui, 2010. "Prediction Errors In Nonstationary Autoregressions Of Infinite Order," Econometric Theory, Cambridge University Press, vol. 26(3), pages 774-803, June.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:03:p:774-803_99
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    Cited by:

    1. Chen, Yi-Ting & Liu, Chu-An, 2023. "Model averaging for asymptotically optimal combined forecasts," Journal of Econometrics, Elsevier, vol. 235(2), pages 592-607.
    2. Chor-yiu Sin & Shu-Hui Yu, 2019. "Order selection for possibly infinite-order non-stationary time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 187-216, June.
    3. Ing, Ching-Kang & Sin, Chor-yiu & Yu, Shu-Hui, 2012. "Model selection for integrated autoregressive processes of infinite order," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 57-71.

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