Statistical Analysis of Time Series

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Code Completion Credits Range Language
NI-SCR Z,ZK 5 2P+1C Czech
Garant předmětu:
Kamil Dedecius
Kamil Dedecius
Kamil Dedecius
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 (BI-LIN), mathematical analysis (BI-ZMA) and probability and statistics (BI-PST).

Syllabus of lectures:

1. Introduction to time series, exponential smoothing, 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 - ETS models.

Syllabus of tutorials:

1. Introduction, models, forecasting, estimation.

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 understanding of how to use the basic times series modelling theory in engineering problems.

Study materials:

1. Barber, D. et al. : Bayesian Time Series Models. Cambridge University Press, 2011. ISBN 978-0521196765.

2. Simon, S. : Optimal State Estimation: Kalman, H-infnity and Nonlinear Approaches. Wiley, 2017. ISBN 987-0471708582.

3. McCleary, R. et al. : Design and Analysis of Time Series Experiments. Oxford University Press, 2017. ISBN 978-0190661564.

Further information:
Time-table for winter semester 2024/2025:
Time-table is not available yet
Time-table for summer semester 2024/2025:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-06-16
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