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

Imperial College Business School, Imperial College London, London SW7 2AZ, UK; Department of Economics, Queen Mary, University of London, London E14 NS, UK
SSRN Electronic Journal 01/2009; DOI: 10.1016/j.jeconom.2009.02.010
Source: RePEc

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 [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.

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    ABSTRACT: We construct a two-sample test for comparison of long memory parameters based on ratios of two rescaled variance (V/S) statistics studied in Giraitis et al. [L. Giraitis, R. Leipus, A. Philippe, A test for stationarity versus trends and unit roots for a wide class of dependent errors, Econometric Theory 21 (2006) 989–1029]. The two samples have the same length and can be mutually independent or dependent. In the latter case, the test statistic is modified to make it asymptotically free of the long-run correlation coefficient between the samples. To diminish the sensitivity of the test on the choice of the bandwidth parameter, an adaptive formula for the bandwidth parameter is derived using the asymptotic expansion in Abadir et al. [K. Abadir, W. Distaso, L. Giraitis, Two estimators of the long-run variance: beyond short memory, Journal of Econometrics 150 (2009) 56–70]. A simulation study shows that the above choice of bandwidth leads to a good size of our comparison test for most values of fractional and ARMA parameters of the simulated series.
    Journal of Multivariate Analysis 10/2010; · 1.06 Impact Factor
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    ABSTRACT: Nous proposons un test pour comparer le paramètre de longue mémoire de deux processus éventuellement corrélés. Le test est construit à partir de la statistique V/S basée sur deux estimations de la variance asymptotique des sommes partielles. Nous établissons la consistance asymptotique du test. Des simulations illustrent les performances du test sur des petits échantillons et sa sensibilité au paramètre de type fenêtre de la statistique V/S. A partir d'un développement asymptotique de la statistique V/S, nous obtenons un critère adaptatif pour le choix de ce paramètre.
    42èmes Journées de Statistique. 01/2010;

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