Syllabus 2007/2008 FMS110

Syllabus academic year 2007/2008

NON-LINEAR TIME SERIES ANALYSIS

FMS110

Higher education credits: 7,5. Grading scale: TH. Level: A (Second level). Language of instruction: The course will be given in English on demand. FMS110 overlap following cours/es: MAS222, MAS222 och MASM12. Optional for: D4, E4, F4, F4sfm, I4, Pi3. Course coordinator: Director of studies, Anna Lindgren, anna@maths.lth.se, Matematisk statistik. Recommended prerequisits: FMS045 Stationary Stochastic Processes and preferably also FMS051 Time Series Analysis. The course might be cancelled if the numer of applicants is less than 16. Assessment: Written and oral project presentation and compulsory presence at the computer exercises. The course grade is based on the project grade. The project can be presented at one of two presentation seminars. Further information: The course is given jointly by Mathematical statistics, LTH and Informatik og Matematisk Modellering at Denmark Technical University in Lyngby. Lectures are given alternatively in Lyngby and Lund, computer exercises in Lund. The course is also given at the faculty of science with the code MAS222. Home page: http://www.maths.lth.se/matstat/kurser/fms110mas222/.

Aim
The course builds on the acknowledgement that a large part of the technical and non-technical systems one encounters as a Master of Engineering contains non-linearities or non-stationary events, that reflects fundamental properties in the studied system. When describing such a system and then using the description for, e.g. prediction or adjustment, it is therefore necessary that the model also describes the non-linear and non-stationary parts of the system. Hence, the course aim is to give fundamental knowledge in modelling of non-linear and non-stationary dynamic, stochastic systems, as well as in the use of stochastic differential equations for modelling physical systems.

Knowledge and understanding
For a passing grade the student must

be able to explain qualitative differences between linear and non-linear models,
be able to distinguish between the properties of parametric and non-parametric models,
understand stochastic filtering of latent processes using Kalman filters and particle filters,
be able to apply methods useful when data is non-stationary.

Skills and abilities
For a passing grade the student must

be able to determine whether data needs to be modelled using a non-linear model,
be able to fit a suitable model to data using different methods,
be able to solve all the parts of a modelling problem using scientific, technical and statistical theory (from this course and other courses) where the solution includes model specification, inference and model choice,
present the solution in a technical report.

Judgement and approach
For a passing grade the student must

be able to utilise scientific articles within the field and related fields.

Contents
Different types of non-linear time series models. Non-parametric estimates of non-linearities, i.a. using kernel estimates. Identification of model structure using parametric and non-parametric methods, parameter estimation. State models for non-linear systems, filtering. Prediction in non-linear systems. Modelling using non-linear stochastic differential equations. Recursive methods for parameter estimation in non-stationary time series. Design of experiments for identification of dynamic systems.

Literature
Madsen, H och Holst, J: Non-linear and Non-stationary Time Series Analysis. Informatics and Mathematical Modelling, Technical University of Denmark, Lyngby, 2006.