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Model selection for integrated autoregressive processes of infinite order

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

Abstract

We show that Akaike’s Information Criterion (AIC) and its variants are asymptotically efficient in integrated autoregressive processes of infinite order (AR(∞)). This result, together with its stationary counterpart established previously in the literature, ensures that AIC can ultimately achieve prediction efficiency in an AR(∞) process, without knowing the integration order.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:106:y:2012:i:c:p:57-71
    DOI: 10.1016/j.jmva.2011.10.008
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    References listed on IDEAS

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    1. Ing, Ching-Kang & Wei, Ching-Zong, 2003. "On same-realization prediction in an infinite-order autoregressive process," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 130-155, April.
    2. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
    3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    4. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
    5. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    6. 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.
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    Cited by:

    1. Gang Cheng & Sicong Wang & Yuhong Yang, 2015. "Forecast Combination under Heavy-Tailed Errors," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    2. Lin, Tzu-Chi & Liu, Chu-An, 2025. "Model averaging prediction for possibly nonstationary autoregressions," Journal of Econometrics, Elsevier, vol. 249(PB).
    3. Liao, Jun & Zou, Guohua & Gao, Yan & Zhang, Xinyu, 2021. "Model averaging prediction for time series models with a diverging number of parameters," Journal of Econometrics, Elsevier, vol. 223(1), pages 190-221.
    4. Costantini, Mauro & Kunst, Robert M., 2021. "On using predictive-ability tests in the selection of time-series prediction models: A Monte Carlo evaluation," International Journal of Forecasting, Elsevier, vol. 37(2), pages 445-460.
    5. William Kengne, 2023. "On consistency for time series model selection," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 437-458, July.
    6. 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.

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