The repository is split into 3 different notebooks.

• synthetic_brownian_motion:
  • For analysis of synthetic time series data.
• points_on_circle:
  • For analysis of synthetic data of points sampled from circles.
• making_images:
  • For making the images in the paper.

Most of the functions are in the directory tsi_functions. In general_functions.py, the first thing is to use the filtration_from_points function, which outputs the persistence of a set of points using Gudhi.

Besides this, you can find top_summary_functions in the same script, which is a function that given persitence output of gudhi, computes the TSI and entropy and other statistics.

For time series, there is a separate script containing some functions. It contains bm_summary_functions, which adds two outputs to top_summary_functions, namely the estimation of Geometric Browinian Motion parameters.

Then summary_curve uses one of the two summary_functions to evaluate TSI and entropy and the other methods on a time series. For this it also requires a persistence_func, which takes the price and outputs the persistence. Use either persistence_timedelay or persistence_timesublevel.