(Created 2009-08-11.)

NON-LINEAR TIME SERIES ANALYSIS | FMS110 |

**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.