Course detail

# Time series analysis

Stochastic processes, mth-order probabilty distributions of stochastic processes, characteristics of stochastic process, point and interval estimate of these characteristics, stationary random processes, ergodic processes.
Decomposition of time series -moving averages, exponential smoothing, Winters seasonal smoothing.
The Box-Jenkins approach (linear process, moving average process, autoregressive process, mixed autoregression-moving average process - identification of a model, estimation of parameters, verification of a model).
Spectral density and periodogram.
The use of statistical system STATISTICA and EXCEL for time analysis.

Language of instruction

Czech

Number of ECTS credits

10

Mode of study

Not applicable.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Entry knowledge

Subjects taught in the course DA03, DA62 - Probability and mathematical statistics
Basics of the theory of probability, mathematical statistics and linear algebra - the normal distribution law, numeric characteristics of random variables and vectors and their point and interval estimates, principles of the testing of statistical hypotheses, solving a system of linear equations, inverse to a matrix

Rules for evaluation and completion of the course

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Aims

After the course, the students should understand the basics of the theory of stochastic processes, know what a stochastic process is and when it is determined in terms of probability, know what numeric characteristics are of stochastic processes and they can be estimated. They should be able to decompose a time series, estimate its components and make forecats, judge the periodicity of a process.
Using statistical programs, they should be able to identify Box-Jenkins models, estimate the parameters of a model, judge the adequacy of a model and construct forecasts.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

CIPRA, T. Analýza časových řad s aplikacemi v ekonomii. 1. vyd. Praha: SNTL, 1986. 246 s. (CS)
BROCKWELL, P.J., DAVIS, R.A. Introduction to Time Series and Forecasting. 2nd ed. New York: Springer, 2002. 434 p. ISBN 0-387-95351-5. (EN)
PAPOULIS, A. Random Variables and Stochastic Processes. 3td ed. New York: McGraw-Hill. Inc. 2021. 659 p. ISBN 0-07-366011-6. (EN)

Recommended literature

SHUMWAY, R.H., STOFFER, D.C. Time Series Analysis and Its Applications: With R Examples (Springer Texts in Statistics) 4th ed. New York:Springer, 2017. 575 p. ISBN 3-31-952451-8 (EN)

Classification of course in study plans

• Programme D-P-C-SI (N) Doctoral

branch PST , 2 year of study, winter semester, compulsory-optional
branch FMI , 2 year of study, winter semester, compulsory-optional
branch KDS , 2 year of study, winter semester, compulsory-optional
branch MGS , 2 year of study, winter semester, compulsory-optional
branch VHS , 2 year of study, winter semester, compulsory-optional

• Programme D-K-C-SI (N) Doctoral

branch VHS , 2 year of study, winter semester, compulsory-optional
branch MGS , 2 year of study, winter semester, compulsory-optional
branch PST , 2 year of study, winter semester, compulsory-optional
branch FMI , 2 year of study, winter semester, compulsory-optional
branch KDS , 2 year of study, winter semester, compulsory-optional

• Programme D-K-C-GK Doctoral

branch GAK , 2 year of study, winter semester, compulsory-optional

• Programme D-K-E-CE (N) Doctoral

branch FMI , 2 year of study, winter semester, compulsory-optional
branch KDS , 2 year of study, winter semester, compulsory-optional
branch MGS , 2 year of study, winter semester, compulsory-optional
branch VHS , 2 year of study, winter semester, compulsory-optional
branch PST , 2 year of study, winter semester, compulsory-optional

#### Type of course unit

Lecture

39 hod., optionally

Teacher / Lecturer

Syllabus

1. General concepts of stochastic process. Mth -order probabilty distributions of stochastic process. Characteristics of stochastic process, poin and interval estimate of these characteristics. 2. Stationary process. 3. Ergodic process. 4. Linear regression model. 5. Linear regression model. 6. Decomposition of time series. Regression approach to trend. 7. Moving average. 8. Exponential smoothing. 9. Winter´s seasonal smoothing. 10. Periodical model - spectral density and periodogram. 11. Linear process. Moving average process - MA(q). 12. Autoregressive process - AR(p). 13. Mixed autoregression - moving average process - ARMA(p,q), ARIMA(p,d,q).