Local empirical spectral measure of multivariate processes with long range dependence

Morten Nielsen

Stochastic Processes and their Applications, 2004, vol. 109, issue 1, 145-166

Abstract: We derive a functional central limit theorem for the empirical spectral measure or discretely averaged (integrated) periodogram of a multivariate long range dependent stochastic process in a degenerating neighborhood of the origin. We show that, under certain restrictions on the memory parameters, this local empirical spectral measure converges weakly to a Gaussian process with independent increments. Applications to narrow-band frequency domain estimation in time series regression with long range dependence, and to local (to the origin) goodness-of-fit testing are offered.

Keywords: Brownian; motion; Fractional; ARIMA; Functional; central; limit; theorem; Goodness-of-fit; test; Integrated; periodogram; Long; memory; Narrow-band; frequency; domain; least; squares (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (2)

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Working Paper: Local Empirical Spectral Measure of Multivariate Processes with Long Range Dependence
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