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PřF:M9121 Time Series I - Course Information

## M9121 Time Series I

**Faculty of Science**

autumn 2021

**Extent and Intensity**- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).

Taught in person. **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**- Tue 16:00–17:50 M2,01021
- Timetable of Seminar Groups:

*D. Kraus* **Prerequisites**- Calculus, linear algebra, basics of probability theory and mathematical statistics, theory of estimation and hypotheses testing, linear regression, working 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 comprehensive coverage of selected fundamental 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**- Properties and characteristics of random processes and time series: distribution, strict and weak stationarity, expectation, autocovariance and autocorrelation function.
- Estimation of characteristics of stationary time series and statistical inference about them.
- Modelling of deterministic components (trend, seasonality) using regression, smoothing and decomposition techniques.
- Principles of prediction, algorithms.
- Simple prediction methods: exponential smoothing, Holt and Holt--Winters method.
- Modelling of stationary time series by ARMA models: properties of ARMA models (causality, invertibility), correlation structure of ARMA processes (autocorrelation, partial autocorrelation), prediction in ARMA models (best linear prediction, algorithms, prediction uncertainty and intervals), estimation of parameters of ARMA models (simple methods, maximum likelihood, properties of estimators).
- Extension of ARMA models to seasonal series and nonstationary series with unit roots (SARIMA models).
- Model building and diagnostics.

**Literature**- 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 - 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

*recommended 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 - FORBELSKÁ, Marie.
*Stochastické modelování jednorozměrných časových řad (Stochastic Univariate Time Series Models)*. 1st ed. Brno: Masarykova univerzita, 2009. 251 pp. 4761/Př-3/09-17/31. ISBN 978-80-210-4812-6. info - PRÁŠKOVÁ, Zuzana.
*Základy náhodných procesů.*1. vyd. Praha: Karolinum, 2004. 151 s. ISBN 8024609711. info

*not specified*- CRYER, Jonathan D. and Kung-Sik CHAN.
**Teaching methods**- Lectures, exercises, practical project
**Assessment methods**- Satisfactory oral presentation of the practical project at the exercise session.
- Bonus (non-mandatory) 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].
- Depending on the epidemiological situation, these requirements will be fulfilled in person or online and may be subject to change.
**Language of instruction**- Czech
**Follow-Up Courses****Further Comments**- The course is taught annually.
**Listed among pre-requisites of other courses****Teacher's information**- https://is.muni.cz/auth/el/sci/podzim2021/M9121/index.qwarp

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/autumn2021/M9121