General course objectives:
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.
|A student who has met the objectives of the course will be able to:|
- 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
|, 322, 218, (+45) 4525 3408,
Erik Lindstrom, tlf. +46 462224578,
|02 Department of Informatics and Mathematical Modeling|
|Department of Mathematical Statistics, Lund University|
Registration Sign up:
Transportation to Lund will be organized.
|Non-linear and non-stationary systems, Stochastic differential equations, Non-linear state space models and filters, Modelling dynamic systems, Recursive estimation|