Local empirical spectral measure of multivariate processes with long range dependence
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.
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Volume (Year): 109 (2004)
Issue (Month): 1 (January)
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