New Nonparametric Modeling Methods for High-Dimensional Time Series

点击翻译按钮获取中文摘要

Advances in modern technology have created numerous massive datasets, providing a great amount of information, but also new analysis challenges. The remarkable increase in the amount of data arises not only in the number of observations over time, but also in the number of variables that are simultaneously measured at each time. This results in high-dimensional time series data that are increasingly encountered in many fields, including finance, economics, genomics, social media, biomedical imaging, and so forth. High dimensional time series can be evolutionary, non-normally distributed, and/or heterogeneous. Methods for analyzing these types of data are still in their infancy due to the considerable methodological challenges encountered to describe their complex structure. Because of the intricacies of modern datasets, conventional statistical methods to extract information are often inappropriate. There is an immediate need for efficient and data-driven nonparametric methods to handle these problems. This project seeks to develop new nonparametric modelling methods with theoretical insights for structural change detection, robust estimation, heterogeneity exploration, and dynamic interdependency investigation. The project will help fill methodological gaps by greatly advancing the understanding of the intricacies of high-dimensional time series data. The new flexible methods may can benefit many scientific areas, including public health, medicine, economics, and the social sciences. The overall goal of this project is to develop new flexible statistical methods and theories to address the analytical challenges encountered in describing the evolutionary, non-normal, and heterogeneous features of high-dimensional time series data. This will be done via four inter-connected research topics. (1) A novel three-step method with theoretical guarantees will be developed for structural change detection and identification of factor models by exploiting nonparametric local estimation, shrinkage methods, and grid search techniques. The method can automatically detect breaks (if they exist) and identify their locations. (2) A new paradigm, covariate-assisted quantile latent factor models, is proposed for dimension reduction of high-dimensional time series. The method is robust to heavy-tailed distributions. The model assumptions are very general: the factors are unobserved, and both of the factors and their loadings can vary across quantiles. In addition, the method does not require moment conditions on the errors. (3) A concave fusion method is proposed for exploring heterogeneous functional curves driven by unobserved classes. The method permits structural change detection and heterogeneity exploration, which are difficult problems due to latent processes and the high-dimensional and dependence features in the data. (4) A new dimensionality reduction tool will be devised for a time-varying coefficient vector autoregressive model by exploiting non-centered functional principal component analysis. A novel computational estimation algorithm will be developed by combining proximal algorithms and optimization over Stiefel manifolds. The method can illuminate dynamic relationships in high dimensional nonstationary time series.