Time series analysis
FAST-DA65OptionalDoctoral (3rd cycle)Acad. year: 2017/2018Winter semester2. year of study10 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.
Learning outcomes of the course unit
Mode of delivery
20 % face-to-face, 80 % distance learning
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
Recommended optional programme components
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
Assesment methods and criteria linked to learning outcomes
Language of instruction
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).
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
39 hours, optionally
Teacher / Lecturer