Title

Properties of Predictors for Multivariate Autoregressive Models with Estimated Parameters

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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

vector time series; nonstationary roots; co-integrated series; ordinary least squares; prediction; mean squared error

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2008 Wiley-Blackwell, All rights reserved.


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