Two estimators of the long-run variance

Karim Abadir (), W Distaso and L Giraitis

Discussion Papers from Department of Economics, University of York

Abstract: We deal with the important question of estimating the long-run variance of a stationary sequence. We derive the asymptotic properties of a generalized Newey-West type of estimator in the case of a linear I(d) process. The results show that the bias and asymptotic distribution of the generalized Newey-West estimator depend on the memory parameter d. If the series has long memory then the estimator might even have a non-Gaussian limit distribution. The optimal bandwidth parameter q minimising MSE is derived. Theoretical results explain the large bias observed in simulation studies with arbitrarily chosen q. An alternative estimator is suggested. It has an asymptotic Gaussian distribution and bias which do not depend on d. The estimator is easy to apply and can be used to construct confidence intervals. Simulations confirm the theoretical findings.

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