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Asymptotic Mean Square Prediction Error for an Autoregressive Model with Estimated Coefficients

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  • Taku Yamamoto

Abstract

In this note, a manageable expression for the asymptotic mean square error of predicting more than one‐step ahead from an estimated autoregressive model is derived. The result relies on a useful lemma on matrix differentiation, and differs from recent similar work of Bhansali (1974).

Suggested Citation

  • Taku Yamamoto, 1976. "Asymptotic Mean Square Prediction Error for an Autoregressive Model with Estimated Coefficients," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(2), pages 123-127, June.
    • Handle: RePEc:bla:jorssc:v:25:y:1976:i:2:p:123-127
    DOI: 10.2307/2346680
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    Cited by:

    1. Tae‐Hwan Kim & Stephen J. Leybourne & Paul Newbold, 2004. "Asymptotic mean‐squared forecast error when an autoregression with linear trend is fitted to data generated by an I(0) or I(1) process," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 583-602, July.
    2. João Henrique Gonçalves Mazzeu & Esther Ruiz & Helena Veiga, 2018. "Uncertainty And Density Forecasts Of Arma Models: Comparison Of Asymptotic, Bayesian, And Bootstrap Procedures," Journal of Economic Surveys, Wiley Blackwell, vol. 32(2), pages 388-419, April.
    3. Daniel W. Apley & Hyun Cheol Lee, 2010. "The effects of model parameter deviations on the variance of a linearly filtered time series," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(5), pages 460-471, August.
    4. Greenaway-McGrevy, Ryan, 2015. "Evaluating panel data forecasts under independent realization," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 108-125.
    5. Luisa Bisaglia & Silvano Bordignon, 2002. "Mean square prediction error for long-memory processes," Statistical Papers, Springer, vol. 43(2), pages 161-175, April.
    6. R. Bhansali, 1996. "Asymptotically efficient autoregressive model selection for multistep prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 577-602, September.
    7. Veiga, Helena, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Zeda Li & William W. S. Wei, 2024. "Measuring the advantages of contemporaneous aggregation in forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(5), pages 1308-1320, August.
    9. Naoya Katayama, 2008. "Asymptotic prediction of mean squared error for long-memory processes with estimated parameters," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(8), pages 690-720.

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