Linear Prediction of Long-Range Dependent Time Series

2007/02/16 by Fanny Godet, Godet, Fanny · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.math/0702485

openalex publication_date 2007/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present two approaches for next step linear prediction of long memory time series. The first is based on the truncation of the Wiener-Kolmogorov predictor by restricting the observations to the last k terms, which are the only available values in practice. Part of the mean squared prediction error comes from the truncation, and another part comes from the parametric estimation of the parameters of the predictor. By contrast, the second approach is non-parametric. An AR(k) model is fitted to the long memory time series and we study the error made with this misspecified model.

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