Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Probability Theory and Statistics
- Code
- idosor2u0um17em
- Title
- Analysis of time series 2 (l)
- Usual semester
- Autumn
- ECTS
- 3
- Language
- en
- Learning outcomes
- Knowledge: getting familiar with the modern notions of time series Ability: to understand and use the theory of time series Attitude: the need to extend the mathematical knowledge, to gain new analytic and applied programming skills Autonomy and Responsibility: based on the gained knowledge in time series, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Box-Pierce and Ljung-Box test. Turning point trials. The problem area of differentiation, unit root tests. Estimation of AR process parameters, Yule-Walker estimation, Burg algorithm. Box-Jenkins method for MA process. Durbin-Levinson, Hannan-Rissanen algorithm for ARMA process. Akaike, Bayes and Hannan-Quinn information criterion. Asymptotic properties of the quasi-ML estimation for a GARCH process. Fractionally integrated and self-similar processes. Donsker's theorem, invariance principle, Lamperti's theorem. Fractional Brownian motion, fractional white noise, FARIMA. The effect of the strength of the correlation on the convergence speed and the limit distribution. The Hurst coefficient est. Adjusted range (R/S) statistics and their properties. V/S and KPSS statistics, method of aggregate variance. Spectrum-based estimation and testing of long memory. Parametric estimates of the order of fractional differentiation.. Nonlinear long memory models, LARCH processes. Hidden state processes. Markov Chain Monte Carlo (MCMC) estimators.
- Assessment method
- exam
- Bibliography
- lecture notes