M9121 Random Processes I

Faculty of Science
Autumn 2015
Extent and Intensity
2/0/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 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
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 12:00–13:50 M1,01017
Prerequisites
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 offered to students of any study field.
Course objectives
This course provides a foundation in the theory of stationary processes in both time and spectral domain. After the course, the students should understand the basics of the theory of stationary stochastic processes and use the decomposition techniques relating to random processes.
Syllabus
  • Basic characteristics of random process, properties of the autocovariance function, continuity, differentiation and integration, spectral representation, prediction, estimation of moment characteristics (mean, autocovariance and autocorrelation function), regression modelling of global and local trend, spectral analysis of random process.
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
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems.
Assessment methods
Final oral exam with written preparation (100%).
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2015, recent)
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