Linear Prediction of Long-Memory Processes: Asymptotic Results on Mean-squared Errors

TL;DR

This paper analyzes two methods for linearly predicting long-memory time series, deriving asymptotic mean-squared error behaviors for both a truncated Wiener-Kolmogorov predictor and an AR(k) model fitting approach.

Contribution

It introduces and compares asymptotic error results for both a truncated predictor and an AR(k) model in long-memory process prediction.

Findings

Asymptotic behavior of mean-squared error for truncated predictor derived

Error analysis for AR(k) model fitting in long-memory processes provided

Comparison of two prediction approaches for long-memory series

Abstract

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 values in practice. We derive the asymptotic behaviour of the mean-squared error as $k$ tends to $ + \infty$. By contrast, the second approach is non-parametric. An AR($k$) model is fitted to the long-memory time series and we study the error that arises in this misspecified model.