Higher-Order Kernel Semiparametric M-Estimation of Long Memory

Marc Henry and Peter M Robinson

STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE

Abstract: Econometric interest in the possibility of long memory has developed as a flexible alternative to, or compromise between, the usual short memory or unit root prescriptions, for example in the context of modelling cointegrating or other relationships and in describing the dependence structure of nonlinear functions of financial returns. Semiparametric methods of estimating the memory parameter can avoid bias incurred by misspecification of the short memory component. We introduce a broad class of such semiparametric estimates that also covers pooling across frequencies. A leading "Box-Club" sub-class, indexed by a single tuning parameter, interpolates between the popular local log periodogram and local Whittle estimates, leading to a smooth interpolation of asymptotic variances. The bias of these two estimates also differs to higher order, and we also show how bias, and asymptotic mean square error, can be reduced, across the class of estimates studied, by means of a suitable version of higher-order kernels. We thence calculate an optimal bandwidth (the number of low frequency periodogram ordinates employed) which minimizes this mean squared error. Finite sample performance is studied in a small Monte Carlo experiment, and an empirical application to intra-day foreign exchange returns is included.

Keywords: Long memory; semiparametric methods; higher-order kernel; M-estimation; bias; mean-squared error. (search for similar items in EconPapers)
Date: 2002-09
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Related works:
Journal Article: Higher-order kernel semiparametric M-estimation of long memory (2003)
Working Paper: Higher-order kernel semiparametric M-estimation of long memory (2002)
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Persistent link: https://EconPapers.repec.org/RePEc:cep:stiecm:436

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