PROPERTIES OF PREDICTORS FOR MULTIVARIATE AUTOREGRESSIVE MODELS WITH ESTIMATED PARAMETERS |
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| Authors: | V. A. Samaranayake David P. Hasza |
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| Affiliation: | University of Missouri-Rolla and Boeing Computer Services |
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| Abstract: | Abstract. The k -dimensional p th-order autoregressive processes { Y t} that are either stationary or have one unstable or explosive root are considered. The properties of the s -periods-ahead predictor Ŷ n+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 Ŷ n+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 Ŷ n+s are investigated. |
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| Keywords: | Vector time series nonstationary roots co-integrated series ordinary least squares prediction mean squared error |
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