M9121 Random Precesses I

Faculty of Science
Autumn 2004
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: z (credit).
Teacher(s)
RNDr. Marie Forbelská, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: RNDr. Marie Forbelská, Ph.D.
Timetable
Thu 8:00–9:50 UP1
Prerequisites
Algebra: matrix calculus, vector spaces. Selected topics from Mathematical Analysis: Fourier series. Probability and statistics: random variables and random vectors, their distribution, moment characteristics, independence, linear regression, hypotheses testing. Computer skill: working knowledge of the numerical computing environment MATLAB.
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 7 fields of study the course is directly associated with, display
Course objectives
A classical course of techniques for linear modeling of univariate (preferably discrete-time) random processes. After the basic theoretical introductory concepts illustrated by numerous examples a lot of selected standard parametric and nonparametric methods are dealt with in detail, allowing one to decompose the time series into its basic components: the deterministic one (typically trend and significant harmonics) and the residual noise. In addition many pre- and postprocessing procedures are included assisting one to choose an appropriate model and verify its quality. Exercises to the lecture are located in a computer lab and use MATLAB computing environment allowing the students to get the basic practical skill. They can run demo scripts related to individual topics of the lectures as well as fit models to simulated and real data using a variety of universal procedures. The implemented algorithms are fully transparent to the students and yield unlimited opportunity for their creativity.
Syllabus
  • Random process: definition, examples of typical processes, consistent system of distribution functions, Kolmogorov theorem, gaussian process, moment characteristics (mean, autocovariance and autocorrelation function), strict and weak stationarity, white noise, ergodicity, special cases of stationary random processes, properties of the autocovariance and autocorrelation function, estimated autocovariance and autocorrelation function, the algebraic and statistical interpretation of this estimate.
  • Decomposition model in time series analysis: choice of the model and its identification, the Box-Cox and power transformation, common methods for estimation of the deterministic components comprising both parametric methods (polynomial regression, growth curves etc.) and nonparametric methods (digital filtration, exponential weighting, spline and kernel smoothing, wavelet shrinkage etc.), randomness tests.
  • Identification of the periodic components: the small trend method, moving average method, the simultaneous estimate of the trend and seasonal component using linear regression, discrete Fourier transform, periodogram, periodicity tests.
  • Note: Computer-aided exercises are supported by the system MATLAB.
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
Assessment methods (in Czech)
Výuka: přednáška + cvičení ve formě počítačového praktika. Zápočet: zpracování individuálního projektu.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~vesely/educ_cz.html#cas_rady
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 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2004, recent)
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