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On same-realization prediction in an infinite-order autoregressive process

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  • Ing, Ching-Kang
  • Wei, Ching-Zong
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    Abstract

    Let observations come from an infinite-order autoregressive (AR) process. For predicting the future of the observed time series (referred to as the same-realization prediction), we use the least-squares predictor obtained by fitting a finite-order AR model. We also allow the order to become infinite as the number of observations does in order to obtain a better approximation. Moment bounds for the inverse sample covariance matrix with an increasing dimension are established under various conditions. We then apply these results to obtain an asymptotic expression for the mean-squared prediction error of the least-squares predictor in same-realization and increasing-order settings. The second-order term of this expression is the sum of two terms which measure both the goodness of fit and model complexity. It forms the foundation for a companion paper by Ing and Wei (Order selection for same-realization predictions in autoregressive processes, Technical report C-00-09, Institute of Statistical Science, Academia Sinica, Taipei, Taiwan, ROC, 2000) which provides the first theoretical verification that AIC is asymptotically efficient for same-realization predictions. Finally, some comparisons between the least-squares predictor and the ridge regression predictor are also given.

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    File URL: http://www.sciencedirect.com/science/article/B6WK9-47WD7D9-1/2/4e2d0bdd3a3239dd87176a4e60ed4a57
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 85 (2003)
    Issue (Month): 1 (April)
    Pages: 130-155

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    Handle: RePEc:eee:jmvana:v:85:y:2003:i:1:p:130-155

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    Related research

    Keywords: Autoregressive process Goodness of fit Least squares Model complexity Ridge regression Same-realization prediction;

    References

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    1. R. Bhansali, 1996. "Asymptotically efficient autoregressive model selection for multistep prediction," Annals of the Institute of Statistical Mathematics, Springer, vol. 48(3), pages 577-602, September.
    2. Ing, Ching-Kang, 2003. "Multistep Prediction In Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 19(02), pages 254-279, April.
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    Cited by:
    1. Zhang, Xinyu & Wan, Alan T.K. & Zou, Guohua, 2013. "Model averaging by jackknife criterion in models with dependent data," Journal of Econometrics, Elsevier, vol. 174(2), pages 82-94.
    2. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
    3. Hansen, Bruce E., 2010. "Averaging estimators for autoregressions with a near unit root," Journal of Econometrics, Elsevier, vol. 158(1), pages 142-155, September.
    4. Hwang, Eunju & Shin, Dong Wan, 2014. "Infinite-order, long-memory heterogeneous autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 339-358.
    5. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
    6. Jirak, Moritz, 2014. "Simultaneous confidence bands for sequential autoregressive fitting," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 130-149.

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