Linear prediction of long-range dependent time series

Fanny Godet

ESAIM: Probability and Statistics (2009)

  • Volume: 13, page 115-134
  • ISSN: 1292-8100

Abstract

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We present two approaches for linear prediction of long-memory time series. The first approach consists in truncating the Wiener-Kolmogorov predictor by restricting the observations to the last k terms, which are the only available data in practice. We derive the asymptotic behaviour of the mean-squared error as k tends to +∞. The second predictor is the finite linear least-squares predictor i.e.  the projection of the forecast value on the last k observations. It is shown that these two predictors converge to the Wiener Kolmogorov predictor at the same rate k-1.

How to cite

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Godet, Fanny. "Linear prediction of long-range dependent time series." ESAIM: Probability and Statistics 13 (2009): 115-134. <http://eudml.org/doc/250648>.

@article{Godet2009,
abstract = { We present two approaches for linear prediction of long-memory time series. The first approach consists in truncating the Wiener-Kolmogorov predictor by restricting the observations to the last k terms, which are the only available data in practice. We derive the asymptotic behaviour of the mean-squared error as k tends to +∞. The second predictor is the finite linear least-squares predictor i.e.  the projection of the forecast value on the last k observations. It is shown that these two predictors converge to the Wiener Kolmogorov predictor at the same rate k-1. },
author = {Godet, Fanny},
journal = {ESAIM: Probability and Statistics},
keywords = {Long-memory; linear model; autoregressive process; forecast error; long-memory},
language = {eng},
month = {3},
pages = {115-134},
publisher = {EDP Sciences},
title = {Linear prediction of long-range dependent time series},
url = {http://eudml.org/doc/250648},
volume = {13},
year = {2009},
}

TY - JOUR
AU - Godet, Fanny
TI - Linear prediction of long-range dependent time series
JO - ESAIM: Probability and Statistics
DA - 2009/3//
PB - EDP Sciences
VL - 13
SP - 115
EP - 134
AB - We present two approaches for linear prediction of long-memory time series. The first approach consists in truncating the Wiener-Kolmogorov predictor by restricting the observations to the last k terms, which are the only available data in practice. We derive the asymptotic behaviour of the mean-squared error as k tends to +∞. The second predictor is the finite linear least-squares predictor i.e.  the projection of the forecast value on the last k observations. It is shown that these two predictors converge to the Wiener Kolmogorov predictor at the same rate k-1.
LA - eng
KW - Long-memory; linear model; autoregressive process; forecast error; long-memory
UR - http://eudml.org/doc/250648
ER -

References

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