Defense: Efficient Bayesian Inference on Classical and Quantile Spectral Analysis of Multivariate Time Series

Zhixiong Hu
Statistical Science PhD Candidate
Virtual Event
Raquel Prado

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Description: Spectral analysis has been widely used to characterize the properties of one or more time series in the frequency domain. Accurate inference of spectral density matrices is critical for understanding the structure underlying the components of a given multivariate temporal process, and for revealing potential relationships across its components. However, inference of spectral density matrices suffers from the curse of dimensionality. This dissertation first develops methods to obtain scalable and accurate inference on the spectral density matrix, and functions of this matrix, for high-dimensional stationary time series under a Bayesian framework. Then, we extend the framework to obtain desirable inferences of the time-varying power spectrum and its functions for high-dimensional nonstationary time series. Finally, we further extend the proposed methods to conduct quantile spectral analysis for multivariate stationary time series. All the proposed Bayesian methods are supported by parallel computation and GPU accelerations to obtain desirable inference within an affordable amount of time. Extensive simulation studies and data analysis show that the inferences are accurate and time-efficient, and that our methods are superior compared to the competing methods.