Analiza Szeregów Czasowych

Wykład w języku angielskim w semestrze zimowym. Może być zaliczany jako przedmiot do wyboru na studiach II stopnia na kierunkach Fizyka i Informatyka Stosowana, na studiach doktoranckich oraz przez uczestników programu Kartezjusz/Descartes.
A lecture in fall semester. An elective course for Master and PhD students in Physics or Applied Computer Science and for participants of the Kartezjusz/Descartes programme.

Prediction is very difficult, especially about the future.
attributed to Niels Bohr

Time Series Analysis

The course will be given online only, over MS Teams. I have created a team "Time Series Analysis". You may join the team using the following code: 29yhptc
The proposed time for the lectures is Thursday, 1615. The lectures will start on October 13, 2022.

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

The use of R or Python programming languages in the assignments is recommended, but not required; you may use any programming language or package of your choice.

Lectures
13.10.22 Sampling, Discrete Fourier Transform (DFT) and its properties, Fast Fourier Transform (FFT) algorithm Lecture  1
20.10.22 The convolution, Wiener-Khinchin Theorem, the periodogram, window functions, time-dependent power spectrum of a nonstationary signal Lecture  2
27.10.22 The white noise and the Brownian motion (the random walk), α-stable distributions, the Wiener filter (the optimal filter) Lecture  3
3.11.22 Digital Linear Filters: The transfer function, FIR and IIR filters, role of the phase, simple low- and high-pass filters, moving averages, differentiating filters, examples of filter design. Lecture  4
17.11.22 The autoregressive AR(p) process: definition, the correlation function and the power spectrum; Youle-Walker equation; partial correlations; Akaike Information Criterion; forecasting Lecture  5
Home Assignments
I strongly suggest that you complete these assigment within two weeks after they have been officially published. I do not object to completing them later on, but if you keep putting the assignments off, you may find that you don't have enough time by the end of the term, before the course finishes. I very much prefer you sending me your assignments in pdf format.
27.10.2022 Power spectrum and the Wiener filter
Data files for these assignments: assgn1.txt, assgn2.txt 		Assignment 1
Assignment 2
10.11.2022 Butterworth filter design Assignment 3
17.11.2022 Fitting parameters to AR(p) models
Data file for assignment 4: data45.txt 		Assignment 4
Bibliography:
  • George E. P. Box, Gwylim M. Jenkins, Gregory C. Reinsel, Greta M. Ljung, Time Series Analysis. Forecasting and Control, Fifth Edition, Wiley, 2016
  • Donald B. Percival, Andrew T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000
  • Holger Kantz, Thomas Schreiber, Nonlinear Time Series Analysis, Springer, 1999
  • W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes 3rd Edition: The Art of Scientific Computing

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Copyright © 2009-22 P. F. Góra. All materials published here are copyrighted. Permission is granted to use them for self-study or non-commercial teaching, provided this copyright notice is preserved.