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Estimation Of The Prediction Error Variance And An R2 Measure By Autoregressive Model Fitting

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  • R. J. Bhansali

Abstract

. For predicting the future values of a stationary process {xt} (t= 0, pL 1, pL 2,…) on the basis of its past, two key parameters are the variance V (h), h≥ 1, of the h‐step prediction error and Z(h) ={R(0) ‐ V(h)}/R(0), the corresponding measure, in an R2 sense, of the predictability of the process from its past, where R(0) denotes the process variance. The estimation of V(h) and Z(h) from a realization of T consecutive observations of {xt} is considered, without requiring that the process follows a finite parameter model. Three different autoregressive estimators are examined and are shown to be asymptotically equivalent in the sense that as T∝ they have the same asymptotic normal distribution. The question of bias in estimating these parameters is also examined and a bias correction is proposed. Finite sample behaviour is investigated by a simulation study.

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  • R. J. Bhansali, 1993. "Estimation Of The Prediction Error Variance And An R2 Measure By Autoregressive Model Fitting," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(2), pages 125-146, March.
    • Handle: RePEc:bla:jtsera:v:14:y:1993:i:2:p:125-146
    DOI: 10.1111/j.1467-9892.1993.tb00133.x
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    Cited by:

    1. Proietti, Tommaso & Luati, Alessandra, 2015. "The generalised autocovariance function," Journal of Econometrics, Elsevier, vol. 186(1), pages 245-257.
    2. Alessandra Luati & Tommaso Proietti & Marco Reale, 2012. "The Variance Profile," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 607-621, June.

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