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The Averaged Periodogram Estimator for a Power Law in CoherencyRebecca J. SelaNew York University (NYU) - Leonard N. Stern School of Business Clifford M. HurvichStern School of Business, New York University; New York University (NYU) - Department of Information, Operations, and Management Sciences August 30, 2011 NYU Working Paper No. SOR-2011-01 Abstract: We prove the consistency of the averaged periodogram estimator (APE) intwo new cases. First, we prove that the APE is consistent for negativememory parameters, after suitable tapering. Second, we prove that theAPE is consistent for a power law in the cross-spectrum and thereforefor a power law in the coherency, provided that sufficiently manyfrequencies are used in estimation. Simulation evidence suggests thatthe lower bound on the number of frequencies is a necessary conditionfor consistency. For a Taylor series approximation to the estimator ofthe power law in the cross-spectrum, we consider the rate ofconvergence, and obtain a central limit theorem under suitableregularity conditions.
Number of Pages in PDF File: 40 working papers seriesDate posted: September 29, 2011Suggested CitationContact Information
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