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PřF:M0122 Time Series II - Course Information

## M0122 Time Series II

**Faculty of Science**

Spring 2020

**Extent and Intensity**- 2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
**Teacher(s)**- Mgr. David Kraus, Ph.D. (lecturer)
**Guaranteed by**- doc. PaedDr. RNDr. Stanislav Katina, Ph.D.

Department of Mathematics and Statistics - Departments - Faculty of Science

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable of Seminar Groups**- M0122/01: No timetable has been entered into IS.
**Prerequisites**-
**M9121**Time Series I

Calculus, linear algebra, basics of probability theory and mathematical statistics, theory of estimation and hypotheses testing, linear regression, basic methods of time series analysis, knowledge of R software **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**- Mathematics - Economics (programme PřF, M-AM)
- Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
- Mathematics (programme PřF, N-MA, specialization Applied Mathematics)

**Course objectives**- The course offers a coverage of selected advanced methods and models for time series. The course covers theoretical foundations, statistical models and inference, software implementation, application and interpretation.
**Learning outcomes**- The students will gain a deeper understanding of the methods and their relations and learn to recognize situations that can be addressed by the models discussed in the course, choose an appropriate model, implement it and interpret the results.
**Syllabus**- Multivariate time series: basic characteristics (cross-covariance function) and inference for them, regression between time series, spurious regression and prewhitening, cointegration, unit root tests and cointegration tests.
- Vector autoregressive models: stationarity, cross-correlation, parameter estimation, prediction, Granger causality, cointegration in VAR models.
- State-space models: properties, Kalman filter, likelihood, missing data, Kalman smoother, dynamic linear models.
- Spectral analysis of time series: spectral decomposition of an autocovariance function, spectral density, spectral representation of a stationary process, spectral density of linear filters and ARMA processes, periodogram, estimation of a spectral density (kernel estimation, AR estimation), multivariate spectral analysis.
- Special models: GARCH models, fractional ARIMA models and other models.

**Literature**- BROCKWELL, Peter J. and Richard A. DAVIS.
*Time series :theory and methods*. 2nd ed. New York: Springer-Verlag, 1991. xvi, 577 s. ISBN 0-387-97429-6. info - COWPERTWAIT, Paul S. P. and Andrew V. METCALFE.
*Introductory time series with R*. New York, N.Y.: Springer, 2009. xv, 254. ISBN 9780387886978. info - CRYER, Jonathan D. and Kung-Sik CHAN.
*Time series analysis : with applications in R*. 2nd ed. [New York]: Springer, 2008. xiii, 491. ISBN 9780387759586. info - FORBELSKÁ, Marie.
*Stochastické modelování jednorozměrných časových řad*. 1. vyd. Brno: Masarykova univerzita, 2009. iii, 245. ISBN 9788021048126. info - HAMILTON, James Douglas.
*Time series analysis*. Princeton, N.J.: Princeton University Press, 1994. xiv, 799 s. ISBN 0-691-04289-6. info - SHUMWAY, Robert H. and David S. STOFFER.
*Time Series Analysis and Its Applications: With R Examples*. Third Edition. New York: Springer-Verlag, 2011. doi:10.1007/978-1-4419-7865-3. URL info

- BROCKWELL, Peter J. and Richard A. DAVIS.
**Teaching methods**- Lectures, exercises, practical project
**Assessment methods**- Bonus midterm written exam (score B between 0 and 100).

Final written exam (score F between 0 and 100).

Total score T is defined as 0.75*F + 0.25*max(F,B) rounded to the nearest integer.

Score-to-grade conversion: A for T in [91,100], B for T in [81,90], C for T in [71,80], D for T in [61,70], E for T in [51,60], F for T in [0,50]. **Language of instruction**- Czech
**Further comments (probably available only in Czech)**- Study Materials

The course is taught annually. **Teacher's information**- The lessons are usually in Czech or in English as needed, and the
relevant terminology is always given with English equivalents.
The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/spring2020/M0122