Course Details

Time series analysis

DAB032 course is part of 24 study plans

Ph.D. full-t. program DPC-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-E compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-GK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-E compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-E compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-GK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-GK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-GK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-E compulsory-elective Winter Semester 2nd year 10 credits

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

Ing. Jan Holešovský, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Learning outcomes

Time series analysis is applied and used in numerous fields of civil engineering. The aim of the course is for the students to grasp the essence and basic principles of time series analysis including its applications as well as to acquire the skills necessary to work on their own in solving the problem types listed in the summary.

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

Corequisites

Not required.

Planned educational activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Forms and criteria of assessment

A student will only receive credit if he will solve individual problems assigned by the teacher. The final examination will be only a written one lasting 90 minutes and consisting of 4 problems to calculate.

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.

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

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.

Lecture

3 hours/week, 13 weeks, elective

Syllabus of lectures

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).