ST821: Time Series

Study Board of Science

Teaching language: English
EKA: N370020102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master

STADS ID (UVA): N370020101
ECTS value: 5

Date of Approval: 04-02-2022

Duration: 1 semester

Version: Approved - active

Entry requirements


Academic preconditions

Students taking the course are expected to:

  • have knowledge of mathematical statistics
  • have basic knowledge of some high-level programming language (for example, R, Python, or Julia).

Course introduction

The aim of the course is to give the students a detailed overview of the analysis and forecasting of time series from a theoretical as well as applied perspective. A time series is a data set that is collected sequentially over time and has a natural ordering. Such data sets arise in various fields such as economics, engineering, biology, astrophysics, medicine, etc. The observations are expected to be related to each other and methodologies developed for independent and identically distributed data are no longer valid. The course focuses on the approaches that are used to analyse, model and forecast the dynamics of time series data.

The course builds on the knowledge acquired in the course ST521: Mathematical Statistics (10 ECTS) and gives an academic basis to write a master’s thesis in time series as well as to analyse and forecast data collected sequentially over time in various fields.

In relation to the competence profiles of the degrees i mathematics and applied mathematics it is the explicit focus of the course to:
  • give the competence to handle model building and model calculations;
  • give skills to perform statistical analysis;
  • give theoretical knowledge and practical experience with the application of methods and models from statistics.

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

  • formulate the main problems and challenges of analysing and forecasting time series;
  • describe characteristic features of time series;
  • understand the most important concepts of time series;
  • derive theoretical properties of commonly used models;
  • compare a range of time series models and identify their strengths and weaknesses;
  • choose an appropriate approach to analyse and forecast empirical data;
  • perform practical analysis and forecasting of time series using some high-level programming language;
  • analyse the fit of a time series model;
  • document the results of a statistical analysis in the form of a written report.


The following main topics are contained in the course:

  • examples of time series;
  • classical decomposition model;
  • estimation and elimination of trend and seasonal components;
  • stochastic processes;
  • stationary time series;
  • ARMA, ARIMA, and SARIMA models;
  • autocorrelation and partial autocorrelation;
  • prediction of stationary processes;
  • time series regression models;
  • spectral analysis;
  • conditional heteroskedasticity models (ARCH and GARCH);
  • state-space models and the Kalman recursions;
  • recurrent neural networks for time series forecasting;
  • multivariate time series.


See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)




Two take-home assignments




Second examiner: Internal


7-point grading scale


Full name and SDU username


Normally, the same as teaching language


At least 72 hours for each of the take-home assignments.

Examination aids


ECTS value


Additional information

The students would get 2 take-home assignments (or take-home exams) where they will be asked to solve some theoretical problems as well as some empirical data problems using the programming language of their choice.
Both assignments are covered by the final assessment.

The re-exam consists of a single take-home assignment covering the entire content of the course.

Indicative number of lessons

40 hours per semester

Teaching Method

The teaching activities are reflected in an estimated allocation of the workload of an average student as follows:

  • Intro phase: 28 hours
  • Training phase: 12 hours
In the intro phase a modified version of the classical lecture is employed, where the terms and concepts of the topic are presented, from theory as well as from examples based on actual data. In these hours there is room for questions and discussions.

In the training phase the students work with data-based problems and discussion topics, related to the content of the previous lectures in the intro phase. In these hours there is a possibility of working specifically with selected difficult concepts.

In the study phase the students work independently with problems and the understanding of the terms and concepts of the topic. Questions from the study phase can afterwards be presented in either the intro phase hours or the study phase hours.

Teacher responsible

Name E-mail Department
Vaidotas Characiejus Institut for Matematik og Datalogi


Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration


Offered in


Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.