Fractional Differentiation on Time Series

As described in Advances of Machine Learning by Marcos Prado

SP500 returns

F(X) = X and its (frac) derivatives/antiderivates

The animation shows the derivative operator oscillating between the antiderivative (α=−1: y = ​1⁄2⋅x2) and the derivative (α = +1: y = 1) of the simple function y = x continuously.

Get Started

git clone git@github.com:philipperemy/fractional-differentiation-time-series.git && cd fractional-differentiation-time-series
virtualenv -p python3 venv
source venv/bin/activate
pip install . --upgrade
python frac_diff_sp500.py

References:

• https://www.wiley.com/en-us/Advances+in+Financial+Machine+Learning-p-9781119482086
• https://wwwf.imperial.ac.uk/~ejm/M3S8/Problems/hosking81.pdf
• https://en.wikipedia.org/wiki/Fractional_calculus