Modelling dependence in discrete time (AAM)

Course content


In this course we study some basic topics from classical time series analysis. We show show how second order dependence in a stationary process manifests in the time and in the frequency domains, i.e. in the autocorrelation function and in the spectral density of the data. We discuss the use of ARMA and GARCH models and related statistical problems, including the  estimation of the autocorrelation function, the properties of the periodogram and parameter estimation for ARMA and GARCH processes. We discuss different forms of prediction in a time series. We also consider the extremogram and the extremal index as measures of extremal dependence in a time series. These quantities are useful for describing clusters of extremes.



MSc programme in Actuarial Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics-Economics

Learning outcome



Knowledge:To understand relevant time series models (FARIMA, GARCH, etc.) and their applications, in particular to financial data.

To understand the relation between the autocovariance function and the spectral distribution.

To know basic estimation procedures and their properties.

To know extremal dependence measures in a time series.


At the end of the course the student shall be able to
analyse stationary time-discrete processes in the time domain (autocovariance and autocorrelation functions) and their spectal distribution.
He/she will also be able to use software packages for time series analysis
such as SAS and R. 


The student will be able to read monographs and articles on time series analysis and he/she will be able to conduct independent research on real-life time series data.




5 hours of lectures per week for 9 weeks.

Lecture notes

Basic knowledge of probability theory and stochastic processes.

7,5 ECTS
Type of assessment
Continuous assessment
Two projects (theoretical problems and simulations). Both count for 50%.
Marking scale
passed/not passed
Censorship form
No external censorship
One internal examiner
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 45
  • Exam
  • 50
  • Preparation
  • 111
  • English
  • 206