Title:

# Stochastic Processes

Code:SSP
Ac.Year:2010/2011
Sem:Summer
Curriculums:
ProgrammeField/
Specialization
YearDuty
IT-MSC-2MBI-Elective
IT-MSC-2MBS-Elective
IT-MSC-2MMI-Elective
IT-MSC-2MMM-Compulsory-Elective - group M
IT-MSC-2MPV-Elective
IT-MSC-2MSK-Elective
Language of Instruction:Czech
Credits:4
Completion:credit+exam
Type of
instruction:
Hour/semLecturesSeminar
Exercises
Laboratory
Exercises
Computer
Exercises
Other
Hours:2600130
ExamsTestsExercisesLaboratoriesOther
Points:5100049
Guarantor:Michálek Jaroslav, doc. RNDr., CSc. (UM OSO)
Lecturer:Michálek Jaroslav, doc. RNDr., CSc. (UM OSO)
Faculty:Faculty of Mechanical Engineering BUT
Department:Department of Mathematics, section of Statistics and Optimalization FME BUT

Learning objectives:
The course objective is to make students familiar with principles of theory stochastic processes and models used for analysis of time series as well as with estimation algorithms of their parameters. At seminars students practically apply theoretical procedures on simulated or real data using the software MATLAB. Result is a project of analysis and prediction of real time series.
Description:
The course provides the introduction to the theory of stochastic processes. The following topics are dealt with: types and basic characteristics, covariation function, spectral density, stationarity, examples of typical processes, time series and evaluating, parametric and nonparametric methods, identification of periodical components, ARMA processes. Applications of methods for elaboration of project time series evaluation and prediction supported by the computational system MATLAB.
Knowledge and skills required for the course:
Rudiments of the differential and integral calculus, probability theory and mathematical statistics.
Study literature:

• Cipra, T.: Analýza časových řad s aplikacemi v ekonomii. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1986. 246 s.
• Brockwell, P.J., Davis, R.A.: Time series: Theory and Methods. 2nd edition 1991. Hardcover: Corr. 6th printing, 1998. Springer Series in Statistics. ISBN 0-387-97429-6.
• Hamilton, J.D.: Time series analysis. Princeton University Press, 1994. xiv, 799 s. ISBN 0-691-04289-6.
• Anděl, J.: Statistická analýza časových řad. Praha: SNTL, 1976.
• Ljung, L.: System Identification-Theory For the User. 2nd ed., PTR Prentice Hall: Upper Saddle River, 1999.
• Brockwell, P.J., Davis, R.A.: Introduction to time series and forecasting. 2nd ed., New York: Springer, 2002. xiv, 434 s. ISBN 0-387-95351-5.
Controlled instruction:
Attendance at seminars is controlled and the teacher decides on the compensation for absences.
Exam prerequisites:
Active participation in seminars, demonstration of basic skills in practical data analysis on PC, evaluation is based on the result of personal project.