AdapstSPEC Squared: a Bayesian Method for Locally Adaptive Non-Parametric Spectral Density Estimation for Non-Stationary Time Series

• Activity Number: 439 - Remembering Dr. Joan Staniswalis
• Type: Invited
• Date/Time: Wednesday, July 31, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Memorial
• Author(s): Nicholas James* and Sally Cripps and Ori Rosen
• Companies: Centre for Translational Data Science and University of Sydney and University of Texas at El Paso
• Keywords: Locally adaptive nonparametric regression; Whittle Likelihood ; Nonstationary Time Series; Transdimensional MCMC

Abstract

This paper presents a method for adaptively estimating the spectral density of non-stationary time series. The work is motivated by the AdaptSPEC (Rosen et. al 2012) algorithm, where the underlying nonstationary spectrum is estimated by adaptively dividing the time series into an unknown but finite number of segments. However unlike AdaptSPEC, where a Gaussian Process with a stationary covariance is used as a prior for the spectra, we allow this prior covariance structure to be nonstationary, by adaptively dividing the frequency into locally stationary spectra, so that the resulting estimate is adaptive in both the time and frequency domain. We call this estimate AdaptSPEC-Squared. The technique is extended to provide locally adaptive non-parametric estimates of regression surfaces for other models such as generalized linear models.