To give an introduction to advanced time series analysis. The primary goal to give a thorough knowledge on modelling dynamic systems. Special attention is paid on non-linear and non-stationary systems, and the use of stochastic differential equations for modelling physical systems. The main goal is to obtain a solid knowledge on methods and tools for using time series for setting up models for real life systems.

• Apply methods for building stochastic dynamic models
• Identify the need for a non-linear model
• Identify the need for a non-stationary model
• Knowledge about a number of non-linear and non-stationary model classes
• Establish models in discrete and continuous time
• Differentiate between methods for formulating stochastic models
• Apply stochastics models for prediction
• Knowledge about using stochastic differential equations for modelling
• Apply non-parametric and semi-parametric methods
• Calculate predictions of time series
• Estimate parameters in stochastic dynamic models
• IDocument and present results in a written report.

Non-linear time series models. Kernel estimators and time series analysis. Identification of non-linear models. State space models. Prediction in non-linear models. State filtering. Stochastic differential equations. Estimation of linear and (some) non-linear stochastic differential equations. Experimental design for dynamic identification. Methods for tracking parameters in non-stationary time series. Examples of both non-linear and non-stationary models. Non-linear models and chaos. Model building for real life systems. The final contents of the course will be discussed with the students.

H. Madsen, J. Holst (2007): Modelling Non-Linear and Non-Stationary Time Series, plus a number of articles

International course.