PřF:M9121 Time Series I - Course Information

M9121 Time Series I

Faculty of Science
Autumn 2023

Extent and Intensity

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

Teacher(s)

doc. Mgr. David Kraus, Ph.D. (lecturer)
Mgr. Markéta Zoubková (seminar tutor)

Guaranteed by

doc. Mgr. David Kraus, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science

Timetable

Thu 10:00–11:50 M1,01017

Timetable of Seminar Groups:

M9121/01: Thu 12:00–13:50 MP1,01014, M. Zoubková
M9121/02: Wed 14:00–15:50 MP1,01014, M. Zoubková

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

recommended literature

SHUMWAY, Robert H. and David S. STOFFER. Time Series Analysis and Its Applications: With R Examples. Third Edition. New York: Springer-Verlag, 2011. Available from: https://dx.doi.org/10.1007/978-1-4419-7865-3. URL 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
HYNDMAN, RJ and G ATHANASOPOULOS. Forecasting: principles and practice. 2nd edition. Melbourne, Australia: OTexts, 2018. URL info

not specified

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

Teaching methods