financial.fractional_differentiation

Implementation of fractional differentiation from the book Advances in Financial Machine Learning by Marcos Lopez de Prado.

Fractional differentiation is a technique to make time series stationary while preserving the memory of the original data.

This implementation utilizes a fixed window size to calculate the fractional differentiation. Note that this implementation is a simplified version compared to the one presented in the book by Marcos Lopez de Prado. Here, we do not consider the weight loss. In the book, weight loss is calculated to account for the fact that the initial points in the series carry different amounts of information than the final points.

In the calculation of fractional differentiation, the price is convolved with the weights to obtain the fractional differentiated series. This process enables the transformation of the time series into a stationary form while retaining the memory of the original data.

To determine the optimal degree of differentiation, one needs to find the minimum value of the differentiation degree, a value between 0 and 1, that renders the time series stationary.

Reference

https://www.wiley.com/en-us/Advances+in+Financial+Machine+Learning-p-9781119482086

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3257419

Functions

calculate_weights(→ list[float])	Calculate the weights for fractional differentiation.
fracdiff_fixedwindow(→ list[float])	Calculate the fractional differentiation with a fixed window size.

Module Contents

financial.fractional_differentiation.calculate_weights(degree: float, length: int) → list[float]

Calculate the weights for fractional differentiation.

\[w_{0} = 1 w_{k} = -w_{k-1} * (d - k + 1) / k\]

Parameters

degreefloat

The degree of differentiation.

lengthint

The length of the weights.

Returns

list[float]

The weights for fractional differentiation.

Examples

>>> calculate_weights(0.5, 3)
[1.0, -0.5, -0.125]
>>> calculate_weights(0.5, 4)
[1.0, -0.5, -0.125, -0.0625]

financial.fractional_differentiation.fracdiff_fixedwindow(price_series: collections.abc.Sequence[float], degree: float, window_size: int) → list[float]

Calculate the fractional differentiation with a fixed window size.

Parameters

price_seriesSequence[float]

The price series to calculate the fractional differentiation.

degreefloat

The degree of differentiation.

window_sizeint

The number of past observations used to compute each value.

Returns

list[float]

The fractional differentiated series.

Raises

ValueError

If window_size is greater than the length of price_series.

Examples

>>> price_series = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
>>> fracdiff_fixedwindow(price_series, 0.5, 3)
[nan, nan, nan, 2.25, 2.625, 3.0, 3.375, 3.75, 4.125, 4.5]