PROPERTIES OF PREDICTORS FOR MULTIVARIATE AUTOREGRESSIVE MODELS WITH ESTIMATED PARAMETERS

V. A. Samaranayake and David P. Hasza

Journal of Time Series Analysis, 1988, vol. 9, issue 4, 361-383

Abstract: 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.

Date: 1988
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