High-Dimensional Time Series Models

Course Overview

This course deals with factor models for large cross-sections of time-series (large N environment). We build the argument in steps, starting from the simplest multivariate technique, principal components.

We then discuss “small N” factor models for cross-sectional data and study how to estimate factor models with the EM algorithm.

We then review dynamic “small N” models for time-series, the associated state-space form and the Kalman filter and smoother, which are typically used to estimate those models.
Moving to the “large N” environment, first with cross-sectional data and then with time-series data, we discuss the link between factors and principal components. We clarify the distinction between static and dynamic factors and highlight how “large N” dynamic factor models can be used to perform structural analysis by using techniques similar to those used in Structural VAR models.

In this context, we review several applications, among others, factor augmented VAR models (FAVAR), the construction of business cycle indicators, how to handle the jagged nature of macroeconomic data releases in nowcasting and forecasting exercises, the analysis of monetary policy in real time, the identification of the monetary transmission mechanism, the identification of news shocks to technology.

If time permits, we discuss non-invertibilities and the relation to factor models.

Matlab programs to implement the theoretical methods and replicate the applications studied in class will be made available to students.