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

2017/01/17 by Claudia Kirch, M. C. Edwards, Kirch, Claudia +5 · 2 citations
Economics, Econometrics and Finance · Environmental Science · Mathematics · #62M10 #62M15 #Climate variability and models #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1701.04846

openalex publication_date 2017/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation
• Generalized autoregressive conditional heteroskedasticity

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• Bayesian nonparametric estimation of correlated gravitational wave detector network noise using matrix-gamma process priors
• Bayesian power spectral density estimation for LISA noise based on P-splines with a parametric boost

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