Fractionally Differentiated Features¶

Fractionally Differentiated Features are a technique used to transform time series data in a way that

Example, fractional differencing $y_t - \gamma y_{t-1}$ where $\gamma$ is a fractional value like 0.5.

Why use fractional differencing?

Preserve Long-Term Trends: Fractional differencing allows you to remove short-term noise while maintaining the long-range dependencies that are crucial for accurate forecasts, especially in financial, economic, or stock market data.
Stationarity Without Over-Differencing: It can help make the series stationary without over-differencing, which can lead to loss of information. For example, first differencing (subtracting one previous observation) may eliminate too much of the useful data, but fractional differencing avoids this problem.
Better Model Performance: For certain time series models, like machine learning models (LightGBM, XGBoost), maintaining long-term dependencies can be crucial for predictive accuracy. Fractional differencing can improve model performance by preserving these important correlations.

Note that integer differencing will:

make the data stationary,
it also often results in over-differencing (no memory), which can remove valuable information and hurt model performance