The Averaged Periodogram Estimator for a Power Law in Coherency
Rebecca J. Sela
New York University (NYU) - Leonard N. Stern School of Business
Clifford M. Hurvich
Stern School of Business, New York University; New York University (NYU) - Department of Information, Operations, and Management Sciences
Journal of Time Series Analysis, Vol. 33, Issue 2, pp. 340-363, 2012
We prove the consistency of the averaged periodogram estimator (APE) in two new cases. First, we prove that the APE is consistent for negative memory parameters, after suitable tapering. Second, we prove that the APE is consistent for a power law in the cross‐spectrum and therefore for a power law in the coherency, provided that sufficiently many frequencies are used in estimation. Simulation evidence suggests that the lower bound on the number of frequencies is a necessary condition for consistency. For a Taylor series approximation to the estimator of the power law in the cross‐spectrum, we consider the rate of convergence and obtain a central limit theorem under suitable regularity conditions.
Number of Pages in PDF File: 24
Keywords: Cross spectrum, tapering, long memoryAccepted Paper Series
Date posted: March 7, 2012
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