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Stationary processes. Continuity, differentiation and integration. Spectral representation.
Linear process. Ergodicity, central limit theorems. Prediction and filtration. ARMA models and their statistical analysis.
Last update: T_KPMS (15.05.2013)
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Students gain basic knowledge of the theory of stationary processes in both time and spectral domain. The aim is also to acquaint students with basic statistical properties of time series. Last update: T_KPMS (15.05.2013)
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The subject is terminated with the course credit (zápočet) and exam.
Obtaining the course credit is a necessary condition for taking the exam.
Criteria for obtaining the course credit, common for all the groups, are the following: 1. Obtaining at least 70 % of points from regular homeworks (Moodle); 2. Sucessfully passing two tests during the course, i.e. obtaining at least 70 % of the points in each test. For each test, there will be up to two chances to retake the test (common for all the groups). The planned terms will be announced at the beginning of the semester in the Moodle platform.
Due to multiple activities required during the semester, a retake of the course credit is not possible. Last update: Dvořák Jiří, doc. RNDr., Ph.D. (20.09.2024)
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Anděl J.: Statistická analýza časových řad. SNTL, Praha 1976
Brockwell P.J., Davis R.A.: Time series: Theory and Methods, Springer-Verlag, New York, 1987
Prášková, Z.: Základy náhodných procesů II. Karolinum, 2004.
Last update: T_KPMS (15.05.2013)
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Lecture+exercises. Exercises will be conducted online via Moodle: https://dl1.cuni.cz/course/view.php?id=5361. Last update: Dvořák Jiří, doc. RNDr., Ph.D. (25.09.2020)
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The exam consists of the written and the oral part.
The written part lasts 70 minutes and 3 assignments are given. If the score achieved from the written part is less than 50%, the final grade is "fail".
The oral part of the exam covers the topics in accordance with the sylabus, in the extent presented at the lectures.
Using any type of notes is not allowed during any part of the exam. Last update: Dvořák Jiří, doc. RNDr., Ph.D. (22.02.2023)
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Stationary processes.
Continuity, differentiation and integration.
Spectral representation.
Linear process. Ergodicity, central limit theorems.
Prediction and filtration.
ARMA models and their statistical analysis. Last update: T_KPMS (15.05.2013)
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probability theory (bachelor level), elements of Hilbert spaces theory, L_p spaces, Fourier series, elements of complex analysis, difference equations
Last update: Prášková Zuzana, doc. RNDr., CSc. (23.05.2019)
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