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

Beyond Whittle: Nonparametric correction of a parametric likelihood with a focus on Bayesian time series analysis