The course offers fundamental knowledge in the field of time series analysis and its applications in various domains, most notably economy, engineering as well as natural and social sciences. The students formalize the concept of a time series through notions of discrete-time signals and random processes, in order to acquire knowledge necessary to select an appropriate model for any actual time series in order to represent it compactly, analyze it as well as forecast its future behaviour.

Students will get to know examples of time series (discrete-time signals). They will be able to interpret actual time series as instances of random processes. They will master the estimation and elimination of trend and seasonal component from a time series. They will get familiar with modelling time series with the aim of their compact representation, separation into relevant components as well as forecasting future values. They will focus particularly on ARMA models and, based on the obtained knowledge, they will be able to select an appropriate model of a time series and to solve a given problem in an appropriate computational environment.

Discrete-time time series (signals), z-transform and spectrum. Random processes, stationarity and ergodicity. Introduction to modelling of time series. Estimation and elimination of trend and seasonality. Spectral analysis of time series. ARMA processes and ARMA models, modelling and forecasting with ARMA processes. Nonstationary and seasonal time series models.

The lectures are continuously followed by synchronized auditory and computer exercises. Auditory exercises contain practical problem solving sessions principally related to time series analysis and processing. In the computer lab students obtain practical experience with time series analysis software tools. Through the teaching process, students are constantly motivated to an intensive discussion, problem oriented reasoning, independent study work and active participation in the lecturing process.