High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods

TL;DR

This paper reviews recent advances in high-dimensional time series regression models, focusing on estimation, inference, and applications in statistical learning, with emphasis on theoretical foundations and practical methodologies.

Contribution

It provides a comprehensive overview of limit and asymptotic theories, and discusses applications of statistical learning methods to high-dimensional time series data.

Findings

Main limit theory results for dependent data and covariance structures

Asymptotic theory for models with many covariates

Applications of statistical learning in time series analysis

Abstract

These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional dependent data which is relevant to covariance matrix structures as well as to dependent time series sequences. Second, we present main aspects of the asymptotic theory related to time series regression models with many covariates. Third, we discuss various applications of statistical learning methodologies for time series analysis purposes.