SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Stochastic Processes 2 - NMSA409
Title in English: Náhodné procesy 2
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: winter
E-Credits: 8
Hours per week, examination: winter s.:4/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Zuzana Prášková, CSc.
Class: M Mgr. FPM
M Mgr. FPM > Povinné
M Mgr. PMSE
M Mgr. PMSE > Povinné
Classification: Mathematics > Probability and Statistics
Is pre-requisite for: NMFM507, NMST450, NMST537, NMEK450, NMTP450
Annotation -
Last update: T_KPMS (15.05.2013)
Stationary processes. Continuity, differentiation and integration. Spectral representation. Linear process. Ergodicity, central limit theorems. Prediction and filtration. ARMA models and their statistical analysis.
Aim of the course -
Last update: T_KPMS (15.05.2013)

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.

Course completion requirements -
Last update: RNDr. Jitka Zichová, Dr. (12.10.2017)

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 are announced at the beginning

of the semester on the webpage of the guarrant and tutors.

Due to multiple activities required during the semester a retake of the credit course is excluded.

Literature - Czech
Last update: T_KPMS (15.05.2013)

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.

Teaching methods -
Last update: T_KPMS (15.05.2013)

Lecture+exercises.

Requirements to the exam -
Last update: doc. RNDr. Zuzana Prášková, CSc. (10.10.2017)

The exam consists of the written (minimum score 50% is necessary to continue in) and the oral parts.

The written part lasts 90 minutes and 4 exercises have to be solved in it. If the score achieved from the written part is less than 50%, the exam is graded as "fail".

The oral part of the exam covers the subject matter in accordance with the sylabus, in the extent presented at the lectures.

Syllabus -
Last update: T_KPMS (15.05.2013)

Stationary processes.

Continuity, differentiation and integration.

Spectral representation.

Linear process. Ergodicity, central limit theorems.

Prediction and filtration.

ARMA models and their statistical analysis.

Entry requirements -
Last update: doc. RNDr. Zuzana Prášková, CSc. (23.05.2019)

probability theory (bachelor level), elements of Hilbert spaces theory, L_p spaces, Fourier series, elements of complex analysis,

difference equations

 
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