Syllabus
Basic concepts:
Time series, basic characteristics.
Linear methods:
AR and ARMA models.
Spectral methods, spectral filters, wavelet transform.
Dimensionality reduction techniques, principal component analysis, canonical correlation analysis.
Nonlinear methods:
Nonlinear and chaotic series. Chaoticity and nonlinearity, behavior of nonlinear systems, attractors and strange attractors.
Phase space reconstruction from time series. Time delay method, multivariate approach.
Fractal dimension, correlation integral, average mutual information, Lyapunov exponents, entropy and their quantification from time series.
Tests for nonlinearity in time series. Time reversibility, surrogate data tests.
Method of local models.
Neural networks. Multilayer perceptron, backpropagation of error. RBF neural networks.
Nonlinear principal component analysis.
Annotation
The course presents principles and applications of various time series analysis methods. Traditional linear approaches are shown, as well as techniques suitable for study of nonlinear and chaotic signals.