Dynamic nonparametric learning for nonstationary time series data
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Citation
Abstract
This dissertation focuses on analyzing nonstationary time series data that presents significant challenges to traditional statistical methods due to the changing aspects of the underlying data-generating mechanism, like the mean, variance, and others over time. To address this issue, we propose innovative nonparametric methods, including a stratified penalization method for time-varying regressions, multi-output time-varying regressions, time-varying second-order moment and correlation function estimation, specifically designed for data with evolving dynamics. We provide the theoretical properties of the proposed nonparametric methods and the computing algorithms for obtaining the nonparametric estimations. We also present numerical results and Monte Carlo simulations to examine the finite sample performance. Furthermore, we considered the application of our methods from various fields, such as finance and environmental science, that involved dynamic time series analysis.
Description
2024