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 terms, which are the only available data in practice. We derive the asymptotic behaviour of the mean-squared error as tends to . The second predictor is the finite linear least-squares predictor i.e. the projection of the forecast value on the last observations. It is shown that these two predictors converge to the Wiener Kolmogorov predictor at the same rate .
Mots-clés : Long-memory, linear model, autoregressive process, forecast error
@article{PS_2009__13__115_0, author = {Godet, Fanny}, title = {Linear prediction of long-range dependent time series}, journal = {ESAIM: Probability and Statistics}, pages = {115--134}, publisher = {EDP-Sciences}, volume = {13}, year = {2009}, doi = {10.1051/ps:2008015}, mrnumber = {2502026}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps:2008015/} }
TY - JOUR AU - Godet, Fanny TI - Linear prediction of long-range dependent time series JO - ESAIM: Probability and Statistics PY - 2009 SP - 115 EP - 134 VL - 13 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps:2008015/ DO - 10.1051/ps:2008015 LA - en ID - PS_2009__13__115_0 ER -
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://archive.numdam.org/articles/10.1051/ps:2008015/
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