Analiza Szeregów Czasowych

Wykład w języku angielskim. Może być zaliczany jako przedmiot do wyboru na Informatyce Stosowanej lub wykład fakultatywny na Fizyce.

Due to the COVID-19 pandemics, all lectures take place on-line on the MS Teams platform. I do not object to recording my lectures, provided the access to these recordings is limited to people taking the course and the recordings are not widely distributed over the net.

Prediction is very difficult, especially about the future.

attributed to Niels Bohr

Time Series Analysis

Time Series Analysis attempts to understand the past and predict the future. It belongs to a broad range of Data Science, and its objective is: given a time series, or an ordered, often temporal, string of data points, predict its future values. Time series often arise when monitoring natural or industrial processes, taking consecutive measurements of a quantity or tracking corporate business metrics. Time Series Analysis accounts for the fact that data points taken over time may have an internal structure, such as autocorrelation, trend, or seasonal variations that should be accounted for, but at the same time data points are contaminated by random noise. Methods developed within Time Series Analysis are frequently used in other areas, like signal or image processing.

The course will cover the following subjects: Fast Fourier Transform - the power spectrum - smoothing and denoising - digital linear filters - "classic" linear models (AR, MA, ARMA, ARIMA, GARCH) - fractional models (ARFIMA) - Detrended Fluctuations Analysis - multivariate time series - wavelets - nonlinear prediction.

To complete the course, a student will need to attend the lectures and either

• complete 6 home assignments, or
• complete 2-5 home assignments and take an oral exam.