M5201 Stochastic models of time series

Faculty of Science
Autumn 2012
Extent and Intensity
2/2. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Forbelská, Ph.D. (lecturer)
Mgr. Marie Leváková, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: RNDr. Marie Forbelská, Ph.D.
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 14:00–15:50 M2,01021
  • Timetable of Seminar Groups:
M5201/01: Tue 16:00–17:50 MP1,01014, M. Leváková
M5201/02: Tue 18:00–19:50 MP1,01014, M. Leváková
Prerequisites
Basics of the theory of probability, mathematical statistics, theory of estimation and the testing of hypothesis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 8 fields of study the course is directly associated with, display
Course objectives
This course provides a foundation in the theory of stationary and nonstationary processes in both time and spectral domain. Methods for building AR, MA and ARMA models are discussed. The course also introduces ARIMA and SARIMA models, and briefly touches on state space models and the Kalman filter. After the course, the students should understand the basics of the theory of stationary and nonstationary stochastic processes and should be able to identify Box-Jenkins models, estimate the parameters of a model, judge the adequacy of a model.
Syllabus
  • Basic characteristics of random process, properties of the autocovariance function, spectral representation, prediction, regression modelling of global and local trend, spectral analysis of random process, white noise, linear process, linear filter, Box-Jenkins methodology, AR, MA, ARMA procesess, causality, invertibility, the best linear prediction, modelling of the trend and seasonality by a SARIMA model, state space models, Kalman filter.
Literature
  • BROCKWELL, P.J. and R.A. DAVIS. Time series:Theory and Methods. 2-nd edition 1991. Hardcover: Corr. 6th printing, 1998. Springer Series in Statistics. ISBN 0-387-97429-6. info
  • HAMILTON, James Douglas. Time series analysis. Princeton, N.J.: Princeton University Press, 1994, xiv, 799 s. ISBN 0-691-04289-6. info
  • CIPRA, Tomáš. Analýza časových řad s aplikacemi v ekonomii. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1986, 246 s. URL info
  • ANDĚL, Jiří. Statistická analýza časových řad. Praha: SNTL, 1976. info
Teaching methods
Lectures: theoretical explanation with practical examples
Assessment methods
Lecture. Oral examination.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2011, Autumn 2011 - acreditation, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016.
  • Enrolment Statistics (Autumn 2012, recent)
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