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Properties Of Predictors For Multivariate Autoregressive Models With Estimated Parameters

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  • V. A. Samaranayake
  • David P. Hasza

Abstract

. The k‐dimensional pth‐order autoregressive processes {Yt} that are either stationary or have one unstable or explosive root are considered. The properties of the s‐periods‐ahead predictor Ŷn+s, obtained by replacing the unknown parameters in the expression for the best linear predictor YTn+s by their least‐squares estimators, is shown to be asymptotically equivalent to the optimal predictor except in the explosive case. An expression for the mean squared error of Ŷn+s is derived through terms of order n‐1 for normal stationary processes when the parameters are estimated from the realization to be predicted. In addition, small‐sample properties of Ŷn+s are investigated.

Suggested Citation

  • V. A. Samaranayake & David P. Hasza, 1988. "Properties Of Predictors For Multivariate Autoregressive Models With Estimated Parameters," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(4), pages 361-383, July.
    • Handle: RePEc:bla:jtsera:v:9:y:1988:i:4:p:361-383
    DOI: 10.1111/j.1467-9892.1988.tb00477.x
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    Cited by:

    1. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2017. "A Justification of Conditional Confidence Intervals," Papers 1710.00643, arXiv.org, revised Jan 2019.
    2. Helmut Lütkepohl, 2013. "Vector autoregressive models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 6, pages 139-164, Edward Elgar Publishing.
    3. John W. Galbraith, 1999. "Content Horizons For Forecasts Of Economic Time Series," Departmental Working Papers 1999-01, McGill University, Department of Economics.

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