Master’s studies

Syllabus for Analysis of Time Series



  • 10 credits
  • Course code: 1MS014
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Mathematics A1N, Financial Mathematics A1N
  • Grading system: Fail (U), 3, 4, 5
  • Established: 2007-03-15
  • Established by: The Faculty Board of Science and Technology
  • Revised: 2013-04-24
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 28, 2013
  • Entry requirements: 120 credits including Inference Theory I, or Probability and Statistics and Stochastic Modelling
  • Responsible department: Department of Mathematics

Learning outcomes

In order to pass the course (grade 3) the student should be able to

  • give an account for the concepts stationary time series and autocorrelation and know how to estimate autocorrelation based on an observed time series;
  • apply methods for estimation of trend and seasonal variation in time series;
  • estimate parameters of ARIMA-processes and assess the validity of the fitted models.
  • make predictions, in particular for ARIMA-processes;
  • explain the foundations of spectral theory and how to estimate spectral density;
  • evaluate results from statistical computer software (for example R) for model fitting of time series.


Stationary time series. ARIMA processes. Box–Jenkin’s method for model adaptation. Prediction. Seasonal modelling. Spectral theory, smoothing methods for spectral estimation. Software for analysis of time series. Overview of multivariate models, Kalman-filters och non-linear models such as ARCH- and GARCH-models.


Lectures, problem solving sessions and computer-assisted laboratory work.


Written examination (8 credit points) at the end of the course. Assignments and laboratory work (2 credit points) during the course.

Reading list

Reading list

Applies from: week 30, 2013

  • Shumway, Robert H.; Stoffer, David S. Time series analysis and its applications : with R examples

    Fourth edition: [Cham]: Springer, [2017]

    Find in the library