KMEM2B Mathematical Methods in Economics IIB

Faculty of Economics and Administration
Spring 2009
Extent and Intensity
0/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. Ing. Jan Čapek, Ph.D. (lecturer)
Guaranteed by
prof. Ing. Osvald Vašíček, CSc.
Department of Economics – Faculty of Economics and Administration
Contact Person: Lydie Pravdová
Timetable
Sat 21. 2. 16:20–19:30 VT206, Sat 7. 3. 16:20–19:30 VT206, Sun 29. 3. 12:50–16:15 VT206, Sat 25. 4. 8:30–11:50 VT206, Sat 23. 5. 16:20–19:30 VT206
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course deals with mathematical-statistical approaches to the analysis of economic processes described by time series.
The introductory part of the course acquaints students with the basics of using index numbers and their application in the area of time series.
The course participants are also introduced to methodological starting points and the application of the classic procedures of time series decomposition, based on regression approaches. These are non-adaptive methods of description of the process development by a trend expressed by mathematical curves, and adaptive methods, such as polynomial moving averages and methods of exponential smoothing.
Simple regression methods of removal of seasonal influence in a time series are also covered. Last but not least, this part of the course also explains and applies in practice the procedures of forecasts based on time series smoothed by the above-mentioned methods.
The final part of the course summarizes the gained knowledge and is devoted to the explanation of the process of behaviour of one economic variable on the basis of behaviour of other variables through a quantified, statistically analyzed single-equation model and the use of the model for forecasting the development of explained variables.
Syllabus
  • The course is divided into 5 blocks; each of them consists of several topics.
  • 1. Basic conceptions of time series analysis. Main methods of time series analysis and its goals. Design of simple linear mathematical time series models and their notational system. Linearization of some non-linear models. Transcript of time series models into MS Excel and Matlab. Ordinary least squares. Parameter estimation in linear regression model. Prerequisites of ordinary least squares. Parameter estimate of a linear model in Excel and Matlab.
  • 2. Verification of a fit of model to data. Statistical significance of parameters. Theil's beta coefficient. Comparison of two hypotheses about model design. Statistical significance testing in Excel and Matlab. Error term distribution test. Residuals autocorrelation test. Residuals heteroskedasticity test. Multicolinearity testing. Tests of fulfillment of the prerequisites in Excel and Matlab. Model-based predictions. Significance bands of model-based predictions. Computation of predictions and its significance bands in Excel and Matlab.
  • 3. Time series decomposition. Additive and multiplicative models. Constant, linear and quadratic trend. Polynomial trends in general. Exponential trend. Modified exponential trend. Logistic trend. Estimation of simple trends in Excel and Matlab.
  • 4. Simple estimate of a seasonal component. Regression approach to the estimate of a seasonal component. Dummy variables. Estimate of a seasonal component in Excel and Matlab. Single equation econometric model. Estimate of an econometric model in Excel and Matlab.
  • 5. Polynomial moving averages. Simple exponential smoothing. Double exponential smoothing. An example of a time series model estimate in a model with seasonal component. Forecasting and analysis of results.
Literature
  • NOVÁK, Ilja, Richard HINDLS and Stanislava HRONOVÁ. Metody statistické analýzy pro ekonomy. 2. přepracované vyd. Praha: Management Press, 2000, 259 s. ISBN 80-7261-013-9. info
  • KVASNIČKA, Michal and Dalibor MORAVANSKÝ. Ekonomicko-matematické metody. Brno: Masarykova univerzita Brno, 2004, 116 pp. 1.vyd. ISBN 80-210-3477-7. info
  • HUŠEK, Roman. Základy ekonometrické analýzy. 1. vyd. Praha: Vysoká škola ekonomická v Praze, 1995, 225 s. ISBN 8070791020. info
  • CIPRA, Tomáš. Analýza časových řad s aplikacemi v ekonomii. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1986, 246 s. URL info
  • ARLT, Josef, Markéta ARLTOVÁ and Eva RUBLÍKOVÁ. Analýza ekonomických časových řad s příklady. 1.vyd.Praha: Vysoká škola ekonomická Praha, 2002, 148 pp. ISBN 80-245-0307-7. info
  • GREENE, William H. Econometric analysis. 5th ed. Upper Saddle River, N.J.: Prentice Hall, 2003, xxx, 1026. ISBN 0131108492. info
Assessment methods
The course is concluded with an exam, which consists of a written and an oral part.
Admittance to the exam requires two POTs (projects) handed in before the deadline.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2007, Spring 2008.
  • Enrolment Statistics (recent)
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