Statistical Analysis of Time Series

The course is not on the list Without time-table
Code Completion Credits Range Language
MI-SCR Z,ZK 4 2P+1C Czech
Department of Applied Mathematics

The course deals with the practical use of the basic time series modelling theory in engineering tasks, ranging from economics (stock exchange prices, employment) and industrial problems (modelling of signals and processes) to computer networks (network components load, attacks detection). The students learn to select a convenient process model, estimate its parameters, analyze its properties and use it for forecasting of future or intermediate values. The stress is put on understanding and adoption of the main principles based on practical real-world examples. Both the lab classes and the lectures exploit freely available software packages in order to provide easy and straightforward transfer of students' knowledge from the academic to the real world.


Basic knowledge of linear algebra and mathematical analysis.

Syllabus of lectures:

1. Introduction to time series, Markov processes, examples.

2. Principles of the frequentist and Bayesian probability and statistics - review.

3. Regression and autoregression models, (auto)correlation, (P)ACF, MA modely, estimation.

4. AR models from the Bayesian and frequentist viewpoints.

5. Mixed models ARMA, examples, estimation.

6. ARIMA models, special cases, examples, estimation.

7. ARIMA from the Bayesian viewpoint - structured Bayesian models.

8. Applications and analyses of AR-based models.

9. Discrete linear state-space models, Kalman filter.

10. Discrete nonlinear state-space models, extended Kalman filter, unscented filter.

11. Discrete nonlinear state-space models: sequential importance sampling, resampling, bootstrap particle filter.

12. Discrete nonlinear state-space models: particle filter extensions.

13. Exponential smoothing.

Syllabus of tutorials:

1. Introduction, models, forecasting, estimation, Markov process.

2. Regression and AR model, examples, various estimation methods.

3. ARMA and ARIMA models, examples.

4. Time series from the Bayesian viewpoint, examples.

5. Filtration of linear and nonlinear state-space models with Kalman filter.

6. Filtration of nonlinear models with particle filter.

Study Objective:

The aim of the course is the student's understanding of the time series modelling and their use in practical applications.

Study materials:

1. David Barber et al., Bayesian Time Series Models, Cambridge University Press (2011).

2. David Barber, Bayesian Reasoning and Machine Learning, Cambridge University Press (2012), ISBN 978-0-521-51814-7.

3. R. McCleary at al., Design and Analysis of Time Series Experiments, Oxford Univ. Press (2017).

Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2022-12-09
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