MA122 Time Series II

Faculty of Science
Spring 2001
Extent and Intensity
2/0/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Vítězslav Veselý, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Vítězslav Veselý, CSc.
Prerequisites (in Czech)
M9121 Random Precesses I
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
Linear systems: definition, linear and cyclic convolution, causality and stability, impulse and frequency response, FIR and IIR filters.
The best linear prediction: Hilbert space \( L^2(\Omega,\cal{A},P) \), the best linear prediction as orthogonal projection, Durbin-Levinson algorithm, partial autocorrelation function.
Box-Jenkins methodology (BJM): the series \( Y_t = \sum_{j=-\infty}^{\infty}\psi_j X_{t-j} \), the general convergence theorem and its application to a stationary process including the computation of its mean and autocovariance function, general principles for modeling unkonown system.
ARMA processes as a special case of BJM: causality and invertibility, methods for the computation of the coefficients of the causal and inverted representation and of the autocovariance function of an ARMA$(p,q)$ process.
Searching an ARMA model: AR and MA models as a more simple case, identification, parameter estimation and verification, asymptotic properties of estimates.
SARIMA processes as a special case of BJM: ARIMA models as a more simple case, identification, parameter estimation and verification.
Note: Computer-aided exercises are supported by the system MATLAB.
See http://www.math.muni.cz/~vesely/educ/cr2sylle.ps for more details.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~vesely/educ_cz.html#cas_rady
The course is also listed under the following terms Spring 2000, Autumn 2001.
  • Enrolment Statistics (Spring 2001, recent)
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