Fractional Differentiation for Stationary Financial Machine Learning Features
Summary
The article introduces fractional differentiation as a way to make financial price series more suitable for machine learning while retaining some information about past price levels. Ordinary returns are presented as stationary but memory-poor, while raw prices retain history but may be non-stationary. A real-valued differencing order between these extremes provides a tunable compromise; the proposed target is the smallest order that achieves stationarity.
It explains the generalized binomial weights and their iterative generation, then contrasts expanding windows with fixed-width windows that stop when weights fall below a threshold. Augmented Dickey-Fuller testing is identified as a tool for assessing stationarity, and the article describes selecting an optimal differencing order and integrating the transformation into a feature pipeline. Illustrations compare prices, returns, and a fractionally differenced series, but they are not evidence of improved trading returns. The approach depends on stationarity tests and window choices, and the article provides no guarantee that retained memory is predictive. It is a feature-engineering method, not a standalone trading strategy.
Key ideas
- Integer differencing can produce stationary returns while discarding information about historical price levels.
- Fractional differencing uses a real-valued order to balance stationarity and retained memory.
- The weight sequence can be generated recursively from the preceding weight.
- Fixed-width windows truncate small weights using a threshold, with window length depending on the order and threshold.
- An Augmented Dickey-Fuller test can help identify the smallest differencing order that achieves stationarity.
- Retaining price memory does not by itself establish predictive power or trading profitability.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.