PřF:MA122 Time Series II - Course Information

MA122 Time Series II

Faculty of Science
Spring 2000

Extent and Intensity

2/0/0. Type of Completion: -.

Teacher(s)

doc. RNDr. Vítězslav Veselý, CSc. (lecturer)

Guaranteed by

Prerequisites (in Czech)

Course Enrolment Limitations

The course is only offered to the students of the study fields the course is directly associated with.

fields of study / plans the course is directly associated with

Syllabus

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 2001, Autumn 2001.