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Linear prediction of long-range dependent time series. (English) Zbl 1180.62132

Summary: 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 \( + \infty\). 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 \(k^{-1}\).

MSC:

62M20 Inference from stochastic processes and prediction
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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