A new type of periodogram, called the Laplace periodogram, is derived by replacing least squares with least absolute deviations in the harmonic regression procedure that produces the ordinary periodogram of a time series. An asymptotic analysis reveals a connection between the Laplace periodogram and the zero-crossing spectrum. This relationship provides a theoretical justification for the Laplace periodogram to be used as a nonparametric tool for analyzing the serial dependence of time-series data. Superiority of the Laplace periodogram in handling heavy-tailed noise and nonlinear distortion is demonstrated by simulations. A real-data example shows its great effectiveness for analyzing heart rate variability in the presence of ectopic events and artifacts.
By: Ta-Hsin Li
Published in: RC24473 in 2008
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