Adaptspec: Adaptive Spectral Estimation for Nonstationary Time Series

• Activity Number: 474
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ori Rosen*+ and Sally Wood and David Stoffer
• Companies: The University of Texas at El Paso and Melbourne Business School and University of Pittsburgh
• Keywords: EEG ; Locally stationary time series ; Reversible jump MCMC ; Spectral Estimation ; Whittle Likelihood

Abstract

We propose a method for analyzing possibly nonstationary time series by adaptively dividing the time series into an unknown but finite number of segments and estimating the corresponding local spectra by smoothing splines. The model is formulated in a Bayesian framework, and the estimation relies on reversible jump Markov chain Monte Carlo (RJMCMC) methods. For a given segmentation of the time series, the likelihood function is approximated via a product of local Whittle likelihoods. Thus, no parametric assumption is made about the process underlying the time series. The number and lengths of the segments are assumed unknown and may change from one MCMC iteration to another. The frequentist properties of the method are investigated by simulation, and applications to EEG and the El Nino Southern Oscillation phenomenonare described in detail.