Nonstationarity-extended Whittle Estimation

TL;DR

This paper develops a nonstationarity-extended Whittle estimator for long memory time series with dependent errors, demonstrating its asymptotic normality and improved efficiency over existing methods, supported by simulation results.

Contribution

It introduces a novel nonstationarity-extended Whittle estimation method for fractional processes, including nonstationary cases, with proven asymptotic properties and enhanced efficiency.

Findings

Estimator is asymptotically normal.

Outperforms tapered Whittle estimator in efficiency.

Simulation confirms theoretical advantages.

Abstract

For long memory time series models with uncorrelated but dependent errors, we establish the asymptotic normality of the Whittle estimator under mild conditions. Our framework includes the widely used FARIMA models with GARCH-type innovations. To cover nonstationary fractionally integrated processes, we extend the idea of Abadir, Distaso and Giraitis (2007, Journal of Econometrics 141, 1353-1384) and develop the nonstationarity-extended Whittle estimation. The resulting estimator is shown to be asymptotically normal and is more efficient than the tapered Whittle estimator. Finally, the results from a small simulation study are presented to corroborate our theoretical findings.