  The Whittle likelihood is widely used for Bayesian nonparametric estimation
of the spectral density of stationary time series. However, the loss of
efficiency for non-Gaussian time series can be substantial. On the other hand,
parametric methods are more powerful if the model is well-specified, but may
fail entirely otherwise. Therefore, we suggest a nonparametric correction of a
parametric likelihood taking advantage of the efficiency of parametric models
while mitigating sensitivities through a nonparametric amendment. Using a
Bernstein-Dirichlet prior for the nonparametric spectral correction, we show
posterior consistency and illustrate the performance of our procedure in a
simulation study and with LIGO gravitational wave data.
