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.
Recommended Citation
V. A. Samaranayake and D. P. Hasza, "Properties of Predictors for Multivariate Autoregressive Models with Estimated Parameters," Journal of Time Series Analysis, Wiley-Blackwell, Jan 2008.
The definitive version is available at https://doi.org/10.1111/j.1467-9892.1988.tb00477.x
Department(s)
Mathematics and Statistics
Keywords and Phrases
vector time series; nonstationary roots; co-integrated series; ordinary least squares; prediction; mean squared error
International Standard Serial Number (ISSN)
0143-9782
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2008 Wiley-Blackwell, All rights reserved.
Publication Date
01 Jan 2008
