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Course, academic year 2024/2025
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Time series analysis methods - NMET063
Title: Metody analýzy časových řad
Guaranteed by: Department of Atmospheric Physics (32-KFA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. Mgr. Jiří Mikšovský, Ph.D.
Teacher(s): doc. Mgr. Jiří Mikšovský, Ph.D.
Annotation -
The course presents principles and applications of various time series analysis methods. Traditional linear approaches are shown, as well as techniques suitable for study of nonlinear and chaotic signals.
Last update: Mikšovský Jiří, doc. Mgr., Ph.D. (14.05.2023)
Aim of the course -

To present basic principles of linear and nonlinear time series analysis.

Last update: JIMI/MFF.CUNI.CZ (30.04.2008)
Course completion requirements -

Presenting solution to sample time series analysis problems.

Last update: Mikšovský Jiří, doc. Mgr., Ph.D. (29.04.2020)
Literature -

Pollock D. S. G. (1999): A Handbook of Time-Series Analysis, Signal Processing and Dynamics. Academic Press, 733 pp.

Von Storch H., Zwiers F. W. (1999): Statistical Analysis in Climate Research. Cambridge University Press, 484 pp.

Abarbanel H. D. I. (1996): Analysis of observed chaotic data. Springer, 272 pp.

Kantz H., Schreiber T. (1997): Nonlinear Time Series Analysis. Cambridge University Press, 304 pp.

Last update: JIMI/MFF.CUNI.CZ (21.04.2008)
Teaching methods -

Lecture, complemented by a practical exercise.

In summer semester 2020/2021: via ZOOM at https://cuni-cz.zoom.us/j/6514300600

Last update: Mikšovský Jiří, doc. Mgr., Ph.D. (26.02.2021)
Requirements to the exam - Czech

Udělení zkoušky je vázáno na prezentaci zápočtových úloh; zkouška má formu diskuse nad zápočtovou prezentací a má ověřit znalost použitých technik a jejich souvislostí, v rozsahu daném sylabem.

Last update: Mikšovský Jiří, doc. Mgr., Ph.D. (08.10.2017)
Syllabus -

Basic concepts:

Time series, basic characteristics.

Linear methods:

AR and ARMA models.

Spectral methods, spectral filters, wavelet transform.

Dimensionality reduction techniques, principal component analysis, canonical correlation analysis.

Nonlinear methods:

Nonlinear and chaotic series. Chaoticity and nonlinearity, behavior of nonlinear systems, attractors and strange attractors.

Phase space reconstruction from time series. Time delay method, multivariate approach.

Fractal dimension, correlation integral, average mutual information, Lyapunov exponents, entropy and their quantification from time series.

Tests for nonlinearity in time series. Time reversibility, surrogate data tests.

Method of local models.

Neural networks. Multilayer perceptron, backpropagation of error. RBF neural networks.

Nonlinear principal component analysis.

Last update: JIMI/MFF.CUNI.CZ (30.04.2008)
 
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