Course Details

Time series analysis

Academic Year 2023/24

DA65 course is part of 12 study plans

​ D-P-C-SI (N) / PST Winter Semester 2nd year

​ D-P-C-SI (N) / FMI Winter Semester 2nd year

​ D-P-C-SI (N) / KDS Winter Semester 2nd year

​ D-P-C-SI (N) / MGS Winter Semester 2nd year

​ D-P-C-SI (N) / VHS Winter Semester 2nd year

​ D-K-C-SI (N) / VHS Winter Semester 2nd year

​ D-K-C-SI (N) / MGS Winter Semester 2nd year

​ D-K-C-SI (N) / PST Winter Semester 2nd year

​ D-K-C-SI (N) / FMI Winter Semester 2nd year

​ D-K-C-SI (N) / KDS Winter Semester 2nd year

​ D-K-C-GK / GAK Winter Semester 2nd year

​ D-K-E-SI (N) / PST Winter Semester 2nd year

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.

Course Guarantor

RNDr. Helena Koutková, CSc.

Institute

Institute of Mathematics and Descriptive Geometry

Objective

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.

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).

Prerequisites

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

Language of instruction

Czech

Credits

10 credits

Semester

winter

Forms and criteria of assessment

examination

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

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

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/272110

Lecture

13 weeks, 3 hours/week, elective

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).