ModelReconstruction

Analysis of time series from stochastic processes.

stanpy.py - Stochystical Analysis Python

Based on "Analysis of time series from stochastic processes" (by J.Gradisek, S.Siegert, R.Friedrich, I.Grabec)

StochasticAnalysis.ipynb shows derivation of the code and some examples.

This module provides a class to determine drift- and diffusion-coefficients of n-dimensional time series by using their statistical definition.

Usage

import stanpy as sp

time_series = [[1, 2, ...], [1, 2, ...]] # your time seres you want to analyze

analysis = sp.StochasticAnalysis(time_series)
analysis.analyze()

# drift and diffusion coefficients are now stored in:
analysis.drift()
analysis.diffusion()

# in the 2d case you can visualize them builtin:
analysis.visualize_2d()

# and you can reconstruct your series with choosen initial values:
r = analysis.reconstruct()

# by converting your coefficients into a FPE you might gain more insight:
f = analysis.solve_fpe()

FPE.ipynb - solution of the Fokker-Planck-Equation

The FPE of two cases (Harmonic- and Van-der-Pol-oscilaltor) is being solved by euler integration.

casesBW.ipynb - analyzing covid-19 data of Baden-Württemberg, Germany

Title says it all.