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.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Not applicable.

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

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

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).

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.

Specification of controlled education, way of implementation and compensation for absences

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

Classification of course in study plans

• Programme DKC-S Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DPA-S Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DKA-S Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DPC-S Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DPA-E Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DKA-E Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DPC-E Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DKC-E Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DPC-GK Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DKC-GK Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DPA-GK Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DKA-GK Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DPC-M Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DKA-M Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DKC-M Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DPA-M Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DKA-K Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DPA-K Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DPC-K Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DKC-K Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DPC-V Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DPA-V Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DKC-V Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
• Programme DKA-V Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

eLearning