The objective of this course is to introduce some potential research topics in time series analysis. The major theme of this course will be on studying multivariate time series, some of which is high-dimensional. We will discuss useful tools for analyzing time series for which the data may have multiple measurements for which temporal and cross-sectional dependencies can be confounded. The goal is to identify a better understanding of the dynamic relationship between variables that can improve accuracy of prediction. This course will go over standard analysis of low-dimensional time series data to provide some foundation. Topics include general concepts, fitting of VARMA models, multivariate count time series, principal components, factor analysis and classification/clustering. Based on this background we will discuss estimation for high-dimensional time series data. In doing so we will consider LASSO estimators and its variants. In addition, we will also explore modern machine learning techniques that can be used for time series analysis.

Modern machine learning requires adaptation and experimentation over large, expensive, and/or mixed-type search spaces. Bayesian optimization, which uses a probability model to reason about and carry out experimental design, has in the last four years seen a major shift in its capabilities and performance, and is now widely used throughout industry and academia. This course will first cover the statistical roots of this literature, its connection to Bayesian decision theory, and the required mechanics with Gaussian processes, kernel methods, and optimization. Second, the course will study the fundamentals adaptive experimentation and Bayesian optimization. The third part of the course will cover very recent advances in the literature including trust region optimization, diverse optimization, latent space optimization, etc. Applications will include large scale machine learning systems, molecular design, and more.