Symbolic and Network-based Analysis Tools

In the first part of the course I will do a broad introduction to dynamical systems and standard tools to analyze time series such as Fourier analysis, correlation analysis, Lyapunov exponents, fractal dimensions as well as practical examples.

Then, I will discuss several techniques for univariate analysis:

1. Symbolic methods of time-series analysis, complexity and information measures.
2. Spatio-temporal representation of a time-series.
3. Representation of a time-series as a complex network.

The third part focuses on bivariate analysis:

1. Correlation between two time series.
2. Statistical similarity measures, mutual information, directionality and causality.
3. Applications.

In the last part of the course will address Multivariate analysis:

1. Representation of a set of time series as a complex network.
2. Network characterization and analysis.
3. Applications.