multivariate nonstationary extreme data

Wavelet-Based Modeling of Dependence Structures in Nonstationary Multivariate Time Series

Haibo Wu, Ph.D. Student, Statistics

Nov 4, 15:00 - 17:00

B3 R5209

Wavelets dynamical modeling Time Series Time Series Analysis multivariate nonstationary extreme data multivariate statistics

This thesis develops a unified wavelet-based statistical framework for modeling time-varying, multiscale dependence structures in nonstationary multivariate time series, to establish a rigorous and versatile statistical foundation for wavelet-based dependence analysis, progressing from pairwise crossscale coherence to canonical and partial canonical coherence between sets of signals.

Modeling and Inference for Multivariate Time Series, with Applications to Integer-Valued Processes and Nonstationary Extreme Data

Matheus B. Guerrero, Ph.D. Student, Statistics

Apr 4, 16:00 - 19:00

B4 L5 R5220

statistical methods integer-valued data autoregressive processes multivariate nonstationary extreme data

This Ph.D. research focuses on proposing new statistical methods for two types of time series data: integer-valued data and multivariate nonstationary extreme data. For the former, the researcher proposes a novel approach to building an integer-valued autoregressive (INAR) model that offers the flexibility to specify both marginal and innovation distributions, leading to several new INAR processes. For the latter, the researcher proposes new extreme value theory methods for analyzing multivariate nonstationary extreme data, specifically EEG recordings from patients with epilepsy. Two extreme-value methods, Conex-Connect and Club Exco, are proposed to study alterations in the brain network during extreme events such as epileptic seizures.