Fractional Differentiation and Entropy for Preserving Market Memory
Summary
The document examines the tension between non-stationary price levels, which retain historical information, and integer differencing, which can discard that memory. It introduces long-range dependence and fractional differentiation as a way to seek stationarity while retaining more of a series’ history. A fixed-width implementation truncates fractional-difference weights once they fall below a chosen threshold, limiting computation and avoiding an expanding historical window. The article illustrates how increasing the differentiation degree makes a series appear more stationary while progressively removing memory.
It then connects this transformation to information entropy and machine-learning features, and the excerpt also describes a self-optimizing trading system. A reported EURUSD test of that system used specified settings without genetic optimization and showed growth over the stated interval; this is only a limited demonstration, not evidence of robust performance. The material does not establish that entropy or fractional differentiation yields reliable forecasts across instruments or regimes. Its central practical trade-off is between making data more stationary and preserving potentially useful historical dependence.
Key ideas
- Price levels retain long histories but are non-stationary, while ordinary differencing can remove useful dependence.
- Fractional differentiation offers intermediate transformations between unchanged prices and fully differenced data.
- A fixed-width method drops weights below a threshold to bound the history used in each calculation.
- Increasing the differentiation degree improves stationarity while reducing retained price-level memory.
- The reported trading test is a limited demonstration and does not establish general predictive performance.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.