Course detail

Models of regression and time series

FAST-DA51Acad. year: 2009/2010

Regression function, linear regression model, method of least squares, confidence interval and testing hypotheses in the model.
Analysis of variance - one factor experiments, multiple-factor experiments.
Stochastic processes, distribution 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.
Periodogram.
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).
The use of statistical system STATGRAPHICS and EXCEL for time analysis.

Language of instruction

Czech

Mode of study

Not applicable.

Guarantor

RNDr. Helena Koutková, CSc.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Not applicable.

Prerequisites

Basics of the theory of probability, mathematical statistics and linear algebra - the law od distribution of a random variable and vector, numeric characteristics of random variables and vectors and their point and interval estimates. Principles of testing statistical hypotheses, solution of a system of linear equations, inverse to a matrix.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

Course curriculum

1. Regular linear regression model.
2. Regular linear regression model.
3. Singular linear regression model
4. Analysis of variance - one factor experiments,
5. Analysis of variance - multiple - factor experiments,
6. Fundamental notions of stochastic process.
7. Stationary process. Ergodic process.
8. Decomposition of time series. Regression approach to trend.
9. Moving average.
10. Exponential smoothing.
11. Periodical model - periodogram.
12. Linear process. Moving average process - MA(q).
13. Autoregressive process - AR(p). Mixed autoregression - moving average process - ARMA(p,q).

Work placements

Not applicable.

Aims

Students should understand the essence of regression analysis, know how to calculate point and interval estimates of parameters and regression function and forecasts in the case of a linear regression model. They should be able to judge the adequacy of a model and test hypotheses in the model, know how to perform an analysis of variation.
They should be familiar with the basic concepts of the theory of stochastic processes, know how to estimate the numeric characteristics of stochastic processes, estimate the trend component of a time series and set up foecasts. They should be able to judge the periodicity of a time series. Students should also get acquainted with the basic Box-Jenkins models.

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme D-K-C-SI Doctoral

    branch FMI , 2 year of study, winter semester, elective

  • Programme D-P-C-SI Doctoral

    branch FMI , 2 year of study, winter semester, elective

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

RNDr. Helena Koutková, CSc.