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The averaged periodogram estimator for a power law in coherency
Author(s) -
Sela Rebecca J.,
Hurvich Clifford M.
Publication year - 2012
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2011.00770.x
Subject(s) - mathematics , estimator , consistency (knowledge bases) , periodogram , tapering , central limit theorem , rate of convergence , strong consistency , cross spectrum , limit (mathematics) , spectral density , convergence (economics) , series (stratigraphy) , long memory , mathematical analysis , statistics , econometrics , frequency domain , discrete mathematics , volatility (finance) , paleontology , channel (broadcasting) , computer graphics (images) , economic growth , computer science , electrical engineering , economics , biology , engineering
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.