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Selected chapters in time series analysis
AK Zeitreihenanalyse
Last Updated: 2026-02-05 15:02:32
Abstract
Introduction to state space models. Filtering, smoothing and parameter estimation: Exact recursive computations in discrete and linearGaussian models. Markov chain Monte Carlo and particle filter methods for general state space models.Introduction to long range dependece.
Content
The main topic of this course is the use of state space models in time series analysis. These models assume that the observations are incomplete and noisy functions of an unobservable state process with a simple Markovian dynamics. A first part will illustrate the flexibilty of this approach by a number of examples. Then I deal with methods to compute the likelihood and conditional distributions of the state given a stretch of observed values. For linear Gaussian models and for models with discrete state space, recursions can be computed in closed form whereas for more general models one needs some approximations. I will concentrate on sequential Monte Carlo approximations that have received much attention recently. Depending on time and the interest of students, I might discuss models with long range dependence towards the end of the course.
Resources
Literature
J. Durbin and S. J. Koopman, Time Series Analysis by State Space Methods. Oxford University Press, 2001. H. R. Künsch, State Space and Hidden Markov Models. In Complex Stochastic Systems, O.E. Barndorff-Nielsen, D. Cox and C. Klüppelberg, eds. Chapman and Hall,/CRC 2001, 109-173.
General Information
- Language
- English
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | AK Zeitreihenanalyse |
|
2 h weekly |