Spacing and Shape of Peaks in Nonparametric Spectrum Estimates

• Activity Number: 317
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: SSC
• Author(s): Charlotte Haley*+ and David Thomson
• Companies: and Queen's University
• Keywords: Multitaper spectrum ; Spectrum Estimation ; Time Series ; Crossings ; Periodicities ; Solar modes

Abstract

In the spectral analysis of time series, the goal is often to determine the frequency and power contributions of periodic components in noise. Single and multiple taper spectrum estimates are approximately chi-squared distributed, so assigning significance to high peaks is not difficult. The difficulty lies in the rate of false detection. In this study, we compute upcrossing rates for Gaussian white noise spectra of high significance levels and determine the width of these excursions. These results give rise to a new approach to the justification of peaks in processes which appear to have "many lines". We give an example of a natural process which contains hundreds of line components whose frequencies correspond approximately with the normal modes of the sun. We show that the distribution of this spectrum is best described by a mixture model of approximately 68% noncentral and 32% central chi-squared components (lines and noise, respectively), and furthermore that, upon random permutation of the data samples, the detection rate falls to that expected for a Gaussian noise process. These experiments suggest that the peaks are genuine, and exhibit extraordinary correlation structure.