Properties of Predictors for Multivariate Autoregressive Models with Estimated Parameters

V. A. Samaranayake; David P. Hasza

doi:10.1111/j.1467-9892.1988.tb00477.x

Properties of Predictors for Multivariate Autoregressive Models with Estimated Parameters

V. A. Samaranayake
, David P. Hasza

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

<p> 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 &Ycirc;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 &Ycirc;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 &Ycirc;n+s are investigated.</p>

Original language	American English
Journal	Journal of Time Series Analysis
DOIs	https://doi.org/10.1111/j.1467-9892.1988.tb00477.x
State	Published - Jan 1 2008

Keywords

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

Disciplines

Mathematics
Statistics and Probability

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https://doi.org/10.1111/j.1467-9892.1988.tb00477.x

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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 \&Ycirc;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 \&Ycirc;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 \&Ycirc;n+s are investigated.",

keywords = "co-integrated series, mean squared error, nonstationary roots, ordinary least squares, prediction, vector time series",

author = "Samaranayake, \{V. A.\} and Hasza, \{David P.\}",

year = "2008",

month = jan,

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doi = "10.1111/j.1467-9892.1988.tb00477.x",

language = "American English",

journal = "Journal of Time Series Analysis",

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TY - JOUR

T1 - Properties of Predictors for Multivariate Autoregressive Models with Estimated Parameters

AU - Samaranayake, V. A.

AU - Hasza, David P.

PY - 2008/1/1

Y1 - 2008/1/1

N2 - 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 &Ycirc;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 &Ycirc;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 &Ycirc;n+s are investigated.

AB - 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 &Ycirc;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 &Ycirc;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 &Ycirc;n+s are investigated.

KW - co-integrated series

KW - mean squared error

KW - nonstationary roots

KW - ordinary least squares

KW - prediction

KW - vector time series

UR - https://scholarsmine.mst.edu/math_stat_facwork/344

UR - https://doi.org/10.1111/j.1467-9892.1988.tb00477.x

U2 - 10.1111/j.1467-9892.1988.tb00477.x

DO - 10.1111/j.1467-9892.1988.tb00477.x

M3 - Article

JO - Journal of Time Series Analysis

JF - Journal of Time Series Analysis

ER -

Properties of Predictors for Multivariate Autoregressive Models with Estimated Parameters

Abstract

Keywords

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