Multivariate Time Series Analysis

Overview

This is an advanced course for Master students. It covers various aspects relevant for the analysis of multivariate time series. Multivariate time series data occurs in many areas, especially in macroeconomic (e.g., GDP, private consumption and investment for a particular country) and finance (e.g., daily returns for all stocks listed at the Frankfurt stock exchange). Often it is necessary to treat such data as being generated by a multivariate stochastic process to account for relationships that exist between the individual time series.

The course starts with a review of univariate time series issues. Students will learn how to model time series processes using the ARIMA framework. Subsequently, the course covers the basics of multivariate probability distributions and moves on to vector autoregressive (VAR) models. Such models describe the joint behavior of multiple time series. Students will learn how to specify and estimate VAR models and use them for predictive analysis. The course covers in depth the difference between the reduced-form and structural VAR representation. Subsequently, it tackles a range of common methods for the identification of structural shocks in empirical macroeconomics (such as monetary policy shocks or fiscal shocks). It also covers the topics of impulse response function, forecast error variance decomposition, and historical decomposition. Finally, the course covers the basics of multivariate GARCH models, which one can use to describe the volatility of vectors of financial return series.

Students should have solid knowledge of the basics of statistics and econometrics and will profit from prior experience with R or other econometric software packages although we do not require any prior programming skills.

Organization

We regularly teach this course in the summer semester. The course language is English.

The course can be used as a module for the following Master programs:

  • Master in Economics
  • Master in Labour Market and Human Resources
  • Master in Finance, Auditing, Controlling, Taxation (FACT)
  • Master in Marketing
  • Master in Socioeconomics
  • Master in Mathematical Economics

The course consists of weekly lectures (2 SWS) and excercise sessions (2 SWS). The latter focus primarily on the implementation of the covered methods in R.

In the summer term 2025, the course is taught by Dr. Maximilian Böck.

The course is worth 5 ECTS which can be earned by passing a written exam (60 minutes) at the end of the semester. (Students can improve their grade by doing a replication study during the semester.)

Syllabus

More information about dates, grading, the software that is used, and the course in general can be found in the syllabus (for summer term 2025).