On the analysis of multivariate time series with specializations on multi-output regression models and two-sample testing
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Abstract
The dissertation aims to develop new statistical inference protocols and their associated asymptotic theory for multivariate time series. Firstly, we address the problem of variable labeling and estimation for multi-output time-varying coefficient models. In these models, the regression coefficient can change over time as a nonparametric function, capturing the time-varying nature of the data. As a result, variables can be classified as time-varying, time-constant, or irrelevant within a nested structure. A variable is considered time-constant or irrelevant if its coefficient function is consistently a constant or zero, respectively, for all outputs. We propose a stratified penalization method that achieves accurate tricategory labeling in a single step. We establish the theoretical properties of this method, including its estimation and labeling consistency. Monte Carlo simulations demonstrate that our proposed method improves the accuracy of labeling and estimation compared to existing methods. Next, we proceed to investigate two-sample inference for time series, specifically considering cases where the compared time series may have staggered observation periods and exhibit joint dependence. We introduce a warped self-normalized subsampling test for strongly mixing data, showing that this approach can be utilized not only for comparing means between two samples but also for comparing other quantities such as variances or quantiles in a unified manner. The associated asymptotic theory is established. We conduct numerical experiments, including Monte Carlo simulations and a real data analysis, to further illustrate the effectiveness of our proposed method.
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2024