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

Imperial College Business School, Imperial College London, London SW7 2AZ, UK
SSRN Electronic Journal 01/2009; 150(1):56-70. DOI: 10.1016/j.jeconom.2009.02.010
Source: RePEc


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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Available from: Karim M. Abadir, Dec 26, 2013
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    • "Under some general conditions these estimators are all log(n)-consistent for d. One can use the HAC estimator of the long run variance v(1) (Abadir et al. (2009)). An estimator of v(φ) is presented in Sec.4 below. "
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    • "Namely, we first estimate d i and then we fit an AR process to (1 − L) ˆ d i X i using the BIC criterion. From Abadir et al. (2009, Theorem 2.1) under similar assumptions on X i as in Section 2 we have the following expansion of S ii,q : for 0 < d i < "
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    Full-text · Article · Oct 2010 · Journal of Multivariate Analysis
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    • ") is not the only way for estimating Ω 11·2 : another option is to constructˆΩ 11·2 from a consistent estimate of Ω. Estimation of Ω can be achieved with HAC-type or Robinson's MAC estimator (for a comparison see Abadir et al. (2009)). "

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