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A functional limit theorem for tapered empirical spectral functions

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  • Dahlhaus, Rainer

Abstract

Using convolution properties of frequency-kernels and their upper bounds we obtain some new upper bounds for the cumulants of time series statistics. From these results we derive the asymptotic normality of some spectral estimates and the tightness of tapered empirical spectral functions in the space of Lipschitz-continuous functions. It follows that tapering increases the asymptotic variance of the estimates by a constant factor. All results are proved under integrability conditions on the spectra. A functional limit theorem for the empirical spectral function is also given without assuming all moments of the underlying process to exist.

Suggested Citation

  • Dahlhaus, Rainer, 1985. "A functional limit theorem for tapered empirical spectral functions," Stochastic Processes and their Applications, Elsevier, vol. 19(1), pages 135-149, February.
    • Handle: RePEc:eee:spapps:v:19:y:1985:i:1:p:135-149
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