Two Estimators of the Long-Run Variance: Beyond Short Memory

38 Pages Posted: 14 Jan 2012

See all articles by Karim M. Abadir

Karim M. Abadir

Imperial College Business School

Walter Distaso

Imperial College Business School

Liudas Giraitis

University of York - Department of Mathematics and Economics

Date Written: January 19, 2009

Abstract

This paper deals with the estimation of the long-run variance of a stationary sequence. We extend the usual Bartlett-kernel heteroskedasticity and autocorrelation consistent (HAC) estimator to deal with long memory and antipersistence. We then derive asymptotic expansions for this estimator and the memory and autocorrelation consistent (MAC) estimator introduced by Robinson (2005). We offer a theoretical explanation for the sensitivity of HAC to the bandwidth choice, a feature which has been observed in the special case of short memory. Using these analytical results, we determine the MSE-optimal bandwidth rates for each estimator. We analyze by simulations the finite-sample performance of HAC and MAC estimators, and the coverage probabilities for the studentized sample mean, giving practical recommendations for the choice of bandwidths.

Suggested Citation

Abadir, Karim M. and Distaso, Walter and Giraitis, Liudas, Two Estimators of the Long-Run Variance: Beyond Short Memory (January 19, 2009). Available at SSRN: https://ssrn.com/abstract=1984844 or http://dx.doi.org/10.2139/ssrn.1984844

Karim M. Abadir (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/portal/page?_pageid=61,629646&_dad=portallive&_schema=PORTALLIVE

Walter Distaso

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

Liudas Giraitis

University of York - Department of Mathematics and Economics ( email )

Heslington, York YO10 5DD
United Kingdom

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