PMCRII Temporal series

Faculty of Economics and Administration
Autumn 2008
Extent and Intensity
2/2. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Vítězslav Veselý, CSc. (lecturer)
doc. RNDr. Vítězslav Veselý, CSc. (seminar tutor)
Guaranteed by
prof. Ing. Osvald Vašíček, CSc.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Timetable
Tue 8:30–10:05 P102
  • Timetable of Seminar Groups:
PMCRII/1: Thu 7:40–9:15 VT206, V. Veselý
Prerequisites
The course is intended for the 2nd year MSc students of the study program "Mathematical and statistical methods in economy".
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 20 student(s).
Current registration and enrolment status: enrolled: 0/20, only registered: 0/20, only registered with preference (fields directly associated with the programme): 0/20
fields of study / plans the course is directly associated with
Course objectives
The purpose of the course is to give a theoretical introduction of the Box-Jenkins methodology. First basics of the theory of linear time-invariant (LTI) systems will be explained which is a theoretical background of the Box-Jenkins methodology involving the commonly used ARMA and ARIMA models for stationary and covariance stationary time series, respectively.
In the stationary case standard techniques for determining the model type and its orders (AR, MA or general ARMA) and the principle of best linear prediction will be explained. For each type parameter estimation concepts will be described along with asymptotic properties of the respective estimates.
Time series II is the second run of a two-term course Time series I-II including a computer-aided tutorial where the students will gain practical skills in time series modeling.
Syllabus
  • The course involves topics as follows.
  • 1. Discrete LTI-systems: impulse and frequency response, causality and stability
  • 2. Mean square convergence of series $Y_t = \sum_{j=-\infty}^{\infty}\psi_j X_{t-j}$
  • 3. Best linear prediction (Yule-Walker system of equations)
  • 4. Partial autocorrelation function
  • 5. ARMA models for stationary time series, AR and MA models as their simpler cases
  • 6. Causality and invertibility for ARMA models
  • 7. Identification, parameter estimation and verification for ARMA models
  • 8. Asymptotic properties of parameter estimates
  • 9. ARIMA and SARIMA models for time series with stationarity defects in the mean
Literature
  • CIPRA, Tomáš. Analýza časových řad s aplikacemi v ekonomii. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1986, 246 s. URL info
  • ANDĚL, Jiří. Statistická analýza časových řad. Praha: SNTL, 1976. info
  • BROCKWELL, Peter J. and Richard A. DAVIS. Introduction to time series and forecasting. 2nd ed. New York: Springer, 2002, xiv, 434. ISBN 0387953515. info
  • HAMILTON, James Douglas. Time series analysis. Princeton, N.J.: Princeton University Press, 1994, xiv, 799 s. ISBN 0-691-04289-6. info
  • BROCKWELL, P.J. and R.A. DAVIS. Time series:Theory and Methods. 2-nd edition 1991. Hardcover: Corr. 6th printing, 1998. Springer Series in Statistics. ISBN 0-387-97429-6. info
  • LJUNG, L. System Identification-Theory For the User. 2nd ed. PTR Prentice Hall: Upper Saddle River, 1999. info
  • LJUNG, L. System Identification Toolbox for use with MATLAB-Users Guide. Natick, 2005. The Maths Works. info
Assessment methods
The course has the form of a lecture (2 lessons) and a computer-aided tutorial (1 lesson), and is concluded by an oral exam. In the course of the tutorial every student has to process an individual project aimed at analysis and modeling of real time series data of their own choice; the assessment of this project becomes a part of the final grading.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
  • Enrolment Statistics (recent)
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