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forecast error

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1 results

Linear prediction of long-range dependent time series
Fanny Godet
Journal:

ESAIM: Probability and Statistics / Volume 13 / July 2009

Published online by Cambridge University Press:

26 March 2009, pp. 115-134

Print publication:

July 2009
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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.