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Abstract
The dependence latent in time series data especially within the tail part versus on average has drawn increasing attention with the aim of investigating concealed data patterns and underlying structures . The inference on such tail dependence could serve as an insightful tool for uncovering the behaviors of extremal value events, in order to provide informed explanations for observed phenomena. This dissertation’s primary objective is to present an analysis of time series sequence from two distinct viewpoints, frequency- domain, and time-domain, both concerning the tail dependence at a high quantile level. To facilitate the analyses, we employ the Tail Adversarial Stability (TAS) framework, which offers a clean and practical framework for studying tail dependent time series.From the frequency-domain point of view, a novel tool of tail spectral density analysis is considered in the double asymptotic setting, which provides a foundational step toward spectral analysis of tail dependent time series. The asymptotic normality results in an effective tool for constructing confidence interval to gauge the uncertainty of tail spectral density estimator. On the other hand, from the time- domain perspective, we adopt a parametric measurement of tail heaviness, known as the tail index, to study the tail behavior of time series sequence. In particular, we consider estimating the tail index under the TAS framework. Extensive simulation studies are conducted to assess the empirical performance from both perspectives. Besides, some data applications are presented to further illustrate the practical implementation.