Approximate variances for tapered spectral estimates

2010/09/14 by Michael Amrein, Amrein, Michael, Hans R. Künsch +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistics Theory (math.ST) #math.ST #stat.CO #stat.TH

paper · pdf · doi:10.48550/arxiv.1009.2698

openalex publication_date 2010/09/14 · arxiv created 2011/01/24 · arxiv updated 2011/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose an approximation of the asymptotic variance that removes a certain discontinuity in the usual formula for the raw and the smoothed periodogram in case a data taper is used. It is based on an approximation of the covariance of the (tapered) periodogram at two arbitrary frequencies. Exact computations of the variances for a Gaussian white noise and an AR(4) process show that the approximation is more accurate than the usual formula.

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