Beyond Whittle's likelihood - new Bayesian semiparametric approaches to time series analysis

• Applicant: Professorin Dr. Claudia Kirch
• Subject Area: Mathematics
• Term: from 2015 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 277714514

Even though nonparametric Bayesian inference has been a rapidly growing topic over the last decade, only very few nonparametric Bayesian approaches to time series analysis have been developed. The main challenge lies in the necessity to specify a likelihood function for Bayesian statistical inference.Several authors solved this problem by using Whittle's likelihood as an approximation for Bayesian modeling of the spectral density as the main nonparametric characteristic of stationary time series. Even for non-Gaussian stationary time series, which are not completely specified by their first and second-order structure, the Whittle likelihood results in asymptotically correct statistical inference in many situations but often at the cost of a loss of efficiency. Parametric models, on the other hand, are more powerful but fail if the model is misspecified. Modern nonparametric bootstrap methods for time series face similar challenges and implicitly use non- or semiparametric approximations of the true likelihood. In this project, we will take advantage of state-of-the-art developments in the bootstrap realm of time series analysis and combine Bayesian parametric time series likelihoods in the time domain with a frequency-domain correction based on nonparametric prior distributions.This yields an entirely new semiparametric approach to Bayesian time series analysis.

• DFG Programme: Research Grants
• International Connection: New Zealand
• Cooperation Partner: Dr. Renate Meyer