M0122 Random Processes II

Faculty of Science
Spring 2010
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Forbelská, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 12:00–13:50 M4,01024
Prerequisites
M9121 Random Processes I
Basics of the theory of probability, mathematical statistics, theory of estimation and the testing of hypothesis, elements of regression and correlation analysis.
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
Course objectives
Basic concepts of linear processes are presented, including stationarity, causality, invertibility, autoregressive moving average models, and forecasting. 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. As a result of successfully completing this course, students should be able to identify Box-Jenkins models, estimate the parameters of a model, judge the adequacy of a model.
Syllabus
  • 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, Peter J. and Richard A. DAVIS. Time series :theory and methods. 2nd ed. New York: Springer-Verlag, 1991, xvi, 577 s. ISBN 0-387-97429-6. info
  • CIPRA, Tomáš. Analýza časových řad s aplikacemi v ekonomii. 1. vyd. Praha: Alfa, Státní nakladatelství technické literatury, 1986, 246 s., ob. info
  • ANDĚL, Jiří. Statistická analýza časových řad. Praha: SNTL, 1976. info
  • HAMILTON, James Douglas. Time series analysis. Princeton, N.J.: Princeton University Press, 1994, xiv, 799 s. ISBN 0-691-04289-6. 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 Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2010, recent)
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