Spectral Density and Spectral Distribution Inference for Long Memory Time Series via Fixed-b Asymptotics

Tucker McElroy () and Dimitris Politis

University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego

Abstract: Recent work in econometrics has provided large bandwidth asymptotic theory for taper-based studentized estimates of the mean, in the context of nonparametric estimation for serially correlated time series data. These taper-based statistics can be viewed as estimates of the spectral density at frequency zero, and hence it is quite natural to extend the asymptotic theory to non-zero frequencies and thereby obtain a large bandwidth theory for spectarl estimation. This approach was developed by Hashimzade and Vogelsang (2008) for the case of a single frequency. This paper extends their work in several ways: (i) we treat multiple frequencies jointly; (ii) we allow for long-range dependence at differing frequencies; (iii) we allow for piecewise smooth tapers, such as trapezoidal tapers; (iv) we develop a theory of higher order accuracy by a novel expansion of the Laplace Transform of the limit distribution. The theoretical results are complemented by simulations of the limit distributions, an application to confidence band construction, and a discussion of the issue of optimal bandwidth selection.

Keywords: Social and Behavioral Sciences; Cyclical Long Memory; Kernel Spectral Estimator; Long Range Dependence; Spectral Confidence Bands (search for similar items in EconPapers)
Date: 2013-01-01
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Journal Article: Spectral density and spectral distribution inference for long memory time series via fixed-b asymptotics (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:cdl:ucsdec:qt6164c110

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