Linear prediction of long-range dependent time series
ESAIM: Probability and Statistics, Tome 13 (2009), pp. 115-134.

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 .

DOI : 10.1051/ps:2008015
Classification : 62M20, 62M10
Mots-clés : Long-memory, linear model, autoregressive process, forecast error 
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     author = {Godet, Fanny},
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     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps:2008015/}
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Godet, Fanny. Linear prediction of long-range dependent time series. ESAIM: Probability and Statistics, Tome 13 (2009), pp. 115-134. doi : 10.1051/ps:2008015. http://www.numdam.org/articles/10.1051/ps:2008015/

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