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).
Teacher(s)
doc. 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:
M9121/01: Wed 10:00–11:50 MP1,01014, 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
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
  • 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. Available from: https://dx.doi.org/10.1007/978-1-4419-7865-3. 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
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
    The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2022, Autumn 2023, Autumn 2024.
    • Enrolment Statistics (autumn 2021, recent)
    • Permalink: https://is.muni.cz/course/sci/autumn2021/M9121