Mathematical Statistics Seminar

Claudia Kirch, University Magdeburg

Frequency Domain Likelihood Approximations for Time Series Bootstrapping and Bayesian Nonparametrics

A large class of time series methods are based on a Fourier analysis, which can be consideredas a whitening of the data, giving rise for example to the famous Whittle likelihood. In particular,frequency domain bootstrap methods have been successfully applied in a large range of situations. Inthis talk, we will rst review existing frequency domain bootstrap methodology for stationary time seriesbefore generalizing them for locally stationary time series. To this end, we rst introduce a movingFourier transformation that captures the time-varying spectral density in a similar manner as the classicalFourier transform does for stationary time series. We obtain consistent estimators for the local spectraldensities and show that the corresponding bootstrap time series correctly mimics the covariance behaviorof the original time series. The approach is illustrated by means of some simulations and an applicationto a wind data set. All time series bootstrap methods are implicitely using a likelihood approximation,which could be used explicitely in a Bayesian nonparametric framework for time series. So far, onlythe Whittle likelihood has been used in this context to get a nonparametric Bayesian estimation of thespectral density of stationary time series. In a second part of this talk we generalize this approach basedon the implicit likelihood from the autoregressive aided periodogram bootstrap introduced by Kreissand Paparoditis (2003). This likelihood combines a parametric approximation with a nonparametriccorrection making it particularly attractive for Bayesian applications. Some theoretic results about thislikelihood approximation including posterior consistency in the Gaussian case are given. The performanceis illustrated in simulations and an application to LIGO gravitational wave data.


  • 24.05.2017 - 24.05.2017
  • 10:00-12:30
  • Weierstrass-Institute for Applied Analysis and Stochastics
  • Event homepage
Speakers

Claudia Kirch, University Magdeburg