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Course, academic year 2023/2024
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Stochastic Processes 2 - NMSA409
Title: Náhodné procesy 2
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023 to 2023
Semester: winter
E-Credits: 8
Hours per week, examination: winter s.:4/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: RNDr. Jiří Dvořák, Ph.D.
doc. RNDr. Daniel Hlubinka, Ph.D.
RNDr. Šárka Hudecová, Ph.D.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinné
Classification: Mathematics > Probability and Statistics
Incompatibility : NMFP403
Is co-requisite for: NMST414
Is incompatible with: NMFP403
Is pre-requisite for: NMEK521, NMEK450, NMFM507, NMTP450
Is interchangeable with: NSTP199, NMFP403, NSTP239
Annotation -
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)
Aim of the course -

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)
Course completion requirements -

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 exactly one chance to retake the test

{one term 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 credit course is excluded.

Last update: Prášková Zuzana, doc. RNDr., CSc. (23.09.2021)
Literature - Czech

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)
Teaching methods -

Lecture+exercises.

Exercises will be conducted online via Moodle: https://dl1.cuni.cz/course/view.php?id=5361.

Last update: Dvořák Jiří, RNDr., Ph.D. (25.09.2020)
Requirements to the exam -

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, RNDr., Ph.D. (22.02.2023)
Syllabus -

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)
Entry requirements -

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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