Course Details
Time series analysis
Academic Year 2024/25
DAB032 course is part of 24 study plans
DKA-E Winter Semester 2nd year
DKA-GK Winter Semester 2nd year
DKA-K Winter Semester 2nd year
DKA-M Winter Semester 2nd year
DKA-S Winter Semester 2nd year
DKA-V Winter Semester 2nd year
DPA-E Winter Semester 2nd year
DPA-GK Winter Semester 2nd year
DPA-K Winter Semester 2nd year
DPA-M Winter Semester 2nd year
DPA-S Winter Semester 2nd year
DPA-V Winter Semester 2nd year
DKC-E Winter Semester 2nd year
DKC-GK Winter Semester 2nd year
DKC-K Winter Semester 2nd year
DKC-M Winter Semester 2nd year
DKC-S Winter Semester 2nd year
DKC-V Winter Semester 2nd year
DPC-E Winter Semester 2nd year
DPC-GK Winter Semester 2nd year
DPC-K Winter Semester 2nd year
DPC-M Winter Semester 2nd year
DPC-S Winter Semester 2nd year
DPC-V 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.
Credits
10 credits
Language of instruction
Czech
Semester
Course Guarantor
Institute
Forms and criteria of assessment
Entry Knowledge
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
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.
Basic Literature
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 Reading
Offered to foreign students
Course on BUT site
Lecture
13 weeks, 3 hours/week, elective
Syllabus
- General concepts of stochastic process. Mth -order probabilty distributions of stochastic process. Characteristics of stochastic process, poin and interval estimate of these characteristics.
- Stationary process.
- Ergodic process.
- Linear regression model.
- Linear regression model.
- Decomposition of time series. Regression approach to trend.
- Moving average.
- Exponential smoothing.
- Winter´s seasonal smoothing.
- Periodical model – spectral density and periodogram.
- Linear process. Moving average process – MA(q).
- Autoregressive process – AR(p).
- Mixed autoregression – moving average process - ARMA(p,q), ARIMA(p,d,q).