Two estimators of the long-run variance: Beyond short memory

Karim M. Abadir , Walter Distaso , Liudas Giraitis

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 [Robinson, P. M., 2005. Robust covariance matrix estimation: HAC estimates with long memory/antipersistence correction. Econometric Theory 21, 171–180]. 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.

Mots clés: C22; C14; Long-run variance; Long memory; Heteroskedasticity and autocorrelation consistent (HAC) estimator; Memory and autocorrelation consistent (MAC) estimator

Karim M. Abadir, Walter Distaso, Liudas Giraitis. Two estimators of the long-run variance: Beyond short memory. Econometrics, 2009, 150 (1), pp.56. ⟨10.1016/j.jeconom.2009.02.010⟩. ⟨hal-00576156⟩