# Linear prediction of long-range dependent time series

ESAIM: Probability and Statistics (2009)

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

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topGodet, 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 -

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