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Course detail

Time series analysis

Course unit code: FAST-DA65
Academic year: 2017/2018
Type of course unit: optional
Level of course unit: Doctoral (3rd cycle)
Year of study: 2
Semester: winter
Number of ECTS credits: 10 
Learning outcomes of the course unit:
Not applicable.
Mode of delivery:
20 % face-to-face, 80 % distance learning
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.
Course contents (annotation):
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.
Recommended or required reading:
ANDĚL, J.: Statistická analýza časových řad. SNTL Praha 1976
CIPRA, T.: Analýza časových řad s aplikacemi v ekonomii. SNTL Praha 1986
KOČENDA, E., ČERNÝ, A.: Elements of time series econometrics an applied approach. Karolinum Praha 2007
PAPOULIS, A.: Random Variables and Stochastic Processes. McGraw-Hill New York 1991
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.

Type of course unit:

Lecture: 39 hours, optionally
Teacher / Lecturer: RNDr. Helena Koutková, CSc.

The study programmes with the given course