Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Modelling dependence in discrete time (AAM)

Practical information
Study year 2016/2017
Block 3
Programme level Full Degree Master
Course responsible
  • Thomas Valentin Mikosch (7-6f6b6d7175656a426f63766a306d7730666d)
Phone: +45 35 30414
Office: 04.3.10
  • Department of Mathematical Sciences
Course number: NMAK14013U

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.


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.




Recommended prerequisites

Basic knowledge of probability theory and stochastic processes.

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


Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)


1 block


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Teaching and learning methods

5 hours of lectures per week for 9 weeks.


No limit




Lecture notes


Category Hours
Lectures 45
Exam 50
Preparation 111
English 206


Type of assessment

Continuous assessment
Two projects (theoretical problems and simulations). Both count for 50%.

Marking scale

passed/not passed

Criteria for exam assessment

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

Censorship form

No external censorship
One internal examiner


Resubmission of the two projects from the continuous assessment. The projects must be resubmitted before 12 noon Friday in the reexamination week.

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