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arXiv · 1701.04846

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

Claudia Kirch·Matthew C. Edwards·Alexander Meier·Renate Meyer
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Abstract

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.

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Claudia Kirch, Matthew C. Edwards, Alexander Meier, Renate Meyer. 2017-01-17. Beyond Whittle: Nonparametric correction of a parametric likelihood with a focus on Bayesian time series analysis. https://arxiv.org/abs/1701.04846

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