The exact multi-period mean-square forecast error for the first-order autoregressive model
type: Item
instance of: scholarly article
title: The exact multi-period mean-square forecast error for the first-order autoregressive model
zbMATH Open document ID: 0668.62070
DOI: 10.1016/0304-4076(88)90062-0
author: Asraul Hoque
author: Jan R. Magnus
author: Bahram Pesaran
published in: Journal of Econometrics
publication date: 1988-01-01T00:00:00Z
full work available at URL: MJHAPB5612872.pdf
review text: The finite-sample behaviour of the multi-period least-squares forecast is considered in the simple normal autoregressive model \(y_ t=\beta y_{t-1}+u_ t\) where \(| \beta | <1\). Necessary and sufficient conditions are established for the existence of the forecast bias and the mean-square forecast error (MSFE) and an exact expression for the MSFE is given. Exact numerical results are obtained for both the stationary and the fixed start-up case. Our main conclusions are that for small values of \(\beta\) the MSFE is a decreasing function of the number of forecast periods, and that the behaviour of the MSFE in the stationary and the fixed start-up case is very similar, except for values of \(| \beta |\) close to 1.
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 62P20
zbMATH DE Number: 4094632
zbMATH Keywords: finite-sample behaviour
zbMATH Keywords: multi-period least-squares forecast
zbMATH Keywords: normal autoregressive model
zbMATH Keywords: forecast bias
zbMATH Keywords: mean-square forecast error
describes a project that uses: nag
describes a project that uses: NAG
MaRDI profile type: Publication
OpenAlex ID: W2133992324
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description: scientific article; zbMATH DE number 4094632