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Laplace Periodogram for Time Series Analysis

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 use of the Laplace periodogram 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 in analyzing heart rate variability in the presence of ectopic events and artifacts.