Analysis of Time Series

10 credits

Syllabus, Master's level, 1MS014

A revised version of the syllabus is available.

Code: 1MS014
Education cycle: Second cycle
Main field(s) of study and in-depth level: Data Science A1N, Financial Mathematics A1N, Mathematics A1N
Grading system: Pass with distinction (5), Pass with credit (4), Pass (3), Fail (U)
Finalised by: The Faculty Board of Science and Technology, 27 August 2009
Responsible department: Department of Mathematics

Entry requirements

120 credits including Inference Theory, or Probability and Statistics and Stochastic Modelling

Learning outcomes

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

be familiar with stationary time series and the autocorrelation of a time series, and know how to estimate autocorrelation based on an observed time series;

know methods for estimation of trend and seasonal variation;

be familiar with some common time series models, in particular ARIMA processes;

be able to estimate the parameters of ARIMA processes and know how to test the validity of the adapted model;

be able to make predictions, in particular for ARIMA processes;

know the foundations of spectral theory and how to estimate spectral density;

possess a basic knowledge of multivariate models, Kalman filters and non-linear models such as ARCH and GARCH models;

be able to use software for analysis and model adaptation of time series.

Content

Stationary time series. ARIMA processes. Box–Jenkin's method for model adaptation. Prediction. Seasonal modelling. Spectral theory, smoothing methods for spectral estimation, Kalman filter. ARCH and GARCH models. Software for analysis of time series.

Instruction

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

Assessment

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