Abstract:
Most nonparametric Bayesian approaches use Whittle's likelihood to estimate the spectral density as the main nonparametric characteristic of stationary time series, as e.g. Choudhuri et al. (2004) and Rosen et al (2012). But as shown in Contreras-Cristan et al. (2006), the loss of e ciency of the nonparametric approach using Whittle's likelihood can be substantial. We show that the Whittle likelihood can be regarded as a special case of a nonparametrically corrected parametric likelihood which gives rise to a robust and more e cient Bayesian nonparametric spectral density estimate based on a generalized Whittle likelihood. Its frequentist properties are investigated in a simulation study. Applications to LIGO gravitational wave data and the El Ni~no Southern Oscillation phenomenon will be described.