Psd: Adaptive, sine multitaper power spectral density estimation for R

Abstract

We present an R package for computing univariate power spectral density estimates with little or no tuning effort. We employ sine multitapers, allowing the number to vary with frequency in order to reduce mean square error, the sum of squared bias and variance, at each point. The approximate criterion of Riedel and Sidorenko (1995) is modified to prevent runaway averaging that otherwise occurs when the curvature of the spectrum goes to zero. An iterative procedure refines the number of tapers employed at each frequency. The resultant power spectra possess significantly lower variances than those of traditional, non-adaptive estimators. The sine tapers also provide useful spectral leakage suppression. Resolution and uncertainty can be estimated from the number of degrees of freedom (twice the number of tapers).This technique is particularly suited to long time series, because it demands only one numerical Fourier transform, and requires no costly additional computation of taper functions, like the Slepian functions. It also avoids the degradation of the low-frequency performance associated with record segmentation in Welch's method. Above all, the adaptive process relieves the user of the need to set a tuning parameter, such as time-bandwidth product or segment length, that fixes frequency resolution for the entire frequency interval; instead it provides frequency-dependent spectral resolution tailored to the shape of the spectrum itself.We demonstrate the method by applying it to continuous borehole strainmeter data from a station in the Plate Boundary Observatory, namely station B084 at the Piñon Flat Observatory in southern California. The example illustrates how psd elegantly handles spectra with large dynamic range and mixed-bandwidth features—features typically found in geophysical datasets.