ESF:PMEM2A Math Methods in Economics II - Course Information

PMEM2A Mathematical Methods in Economics II

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

prof. Ing. Osvald Vašíček, CSc. (lecturer)
doc. Ing. Jan Čapek, Ph.D. (seminar tutor)
doc. Ing. Daniel Němec, Ph.D. (seminar tutor)
Ing. Miroslav Hloušek, Ph.D. (assistant)

Guaranteed by

prof. Ing. Osvald Vašíček, CSc.
Department of Economics – Faculty of Economics and Administration
Contact Person: Lydie Pravdová

Timetable

Thu 11:05–12:45 P101

• Timetable of Seminar Groups:

PMEM2A/1: Wed 17:10–18:45 VT206, J. Čapek
PMEM2A/2: Wed 11:05–12:45 VT206, J. Čapek
PMEM2A/3: Thu 7:40–9:15 VT206, J. Čapek
PMEM2A/4: Thu 9:20–11:00 VT206, J. Čapek
PMEM2A/5: Thu 14:35–16:15 VT105, D. Němec

Prerequisites (in Czech)

PMSTII Statistics II

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

there are 7 fields of study the course is directly associated with, display

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 work with index numbers and their application in the area of time series.
The course participants are also introduced to the methodological premises and the application of the classic procedures of time series decomposition, based on regression. 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 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 next part of the course focuses on the Box-Jenkins methodology of the analysis of time series, using stochastic and correlation properties of time series. These are particularly the methods of moving totals processes analysis (MA), autoregression processes (AR) and mixed processes (ARMA and ARIMA).
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 the explained variable.

Syllabus

• 1. Basal and chained indices, derived indicators.
• 2. Time series decomposition - trend, cyclical, seasonal and random component. Linear regression model. Trend in a time series. Ordinary least squares.
• 3. Polynomial trends, significance bands, forecast, forecast bands.
• 4. Exponential trend, weighted least squares. Modified exponential trend, method of group differences.
• 5. Logistic trend, level of saturation, curves symmetric around inflex point, differential estimate of parameters. Gompertz curve.
• 6. Method of moving averages, derivation of polynomial moving average weights, calculation of initial and final values, calculation of a forecast.
• 7. Exponential smoothing. Single and double exponential smoothing, forecast.
• 8. Analysis of a seasonal component - simple and regression approach.
• 9. Basic conceptions of Box-Jenkins methodology. Autocorrelation properties of time series, stationarity, autocovariance and autocorrelation functions and their estimation, Bartlett approximation, partial autocorrelation function, Quenouill approximation, linear process.
• 10. Moving average process (MA) – variance, autocorrelation functions and estimation of MA parameters.
• 11. Autoregressive process (AR) – variance, autocorrelation functions and estimation of AR parameters.
• 12. Mixed autoregressive process with a moving average process (ARMA) – stationarity, variance, autocorrelation functions and estimation of ARMA parameters. Homogenous non-stationary processes (ARIMA) – homogenous non-stationarity, variance, autocorrelation function.
• 13. Single-equation econometric model - description, parameter estimation, model verification, autocorrelation, multicolinearity.

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
• ARLT, Josef. Moderní metody modelování ekonomických časových řad. Vyd. 1. Praha: Grada, 1999, 307 s. ISBN 8071695394. info
• KVASNIČKA, Michal and Dalibor MORAVANSKÝ. Ekonomicko-matematické metody. Brno: Masarykova univerzita Brno, 2004, 116 pp. 1.vyd. ISBN 80-210-3477-7. info
• CIPRA, Tomáš. Analýza časových řad s aplikacemi v ekonomii. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1986, 246 s. URL info
• PINDYCK, Robert S. and Daniel L. RUBINFELD. Econometric models and economic forecasts. 4th ed. Boston: Irwin, 1997, xx, 634. ISBN 0070502080. info
• ENDERS, Walter. Applied econometric time series. 2nd ed. Hoboken: John Wiley & Sons, 2004, xiv, 460. ISBN 0471230650. info
• HAMILTON, James Douglas. Time series analysis. Princeton, N.J.: Princeton University Press, 1994, xiv, 799 s. ISBN 0-691-04289-6. info
• GREENE, William H. Econometric analysis. 5th ed. Upper Saddle River, N.J.: Prentice Hall, 2003, xxx, 1026. ISBN 0131108492. info

Assessment methods

During the semester: 2 progress tests, one project and reviews on projects of fellow students.
Exam at the end of semester: Written and oral.
More detailed info in IS MU (file rules.pdf)

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.
Information on course enrolment limitations: 10 pouze přednáška

• Enrolment Statistics (recent)
  
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