Zeda Li, Paul H. Chook Department of Information Systems and Statistics, City University of New York, will present, “Adaptive Bayesian Time-Frequency Analysis of Multivariate Time Series”.
Abstract: Understanding cyclical patterns in multiple nonstationary time series, or multivariate time-varying spectral analysis, is important in a variety of fields such as biomedicine, economics, and environmental science. The fundamental unit in multivariate spectral analysis is the power spectrum, a complex matrix valued function of frequency. The complex structure of multivariate time-varying power spectra presents many challenges that have impeded the scope of processes and questions that can be addressed through existing methods. While methods for univariate time series are rather extensive, existing methods for estimating the time-varying spectrum of a multivariate time series are relatively few. This talk has three goals. (1) Discuss the fundamental ideas behind spectral analysis. (2) Discuss the adaptive Bayesian time-frequency analysis of multivariate time series recently introduced by Li and Krafty (2017+) that allows analyzing power spectrum flexibly and efficiently. (3) Explore open research questions in multivariate spectral analysis brought about by complicated modern data structures.