High-Dimensional Time Series
Objectives
Handling multivariate time series, performing a descriptive analysis on time series data, selecting an appro-priate model for multivariate time series, utilizing appropriate methods for statistical inference, prediction or classification of multivariate and high-dimensional time series.
Course outline
In this course, we will introduce the primary tools for analyzing time series data. We will begin by presenting the key concepts for dealing with univariate time series, such as trend, seasonality, and stationary processes. Subsequently, we will delve into the main models and inference methods for multivariate linear time series. In the latter part of the course, we will explore the scenario of multiple time series with a substantial number of components. To address high-dimensional parameter spaces, we will introduce the LASSO penalty and its variants, along with dimension reduction techniques using factor models. Towards the end of the course, we will provide an introduction to neural networks and to clustering or classification problems in the context of time series analysis. Real-world data examples and the software R will be used to illustrate all the methods.
Prerequisites
Basics in probability theory, statistical inference, linear algebra. Knowledge of the software R.