Fractional Differencing and Triple Barriers

Article Hudson & Thames

Summary

This tutorial presents preprocessing and labeling methods for supervised trading models. Fractional differentiation is used to make price features more stationary while retaining more of their historical dependence than ordinary differencing may preserve. The tutorial describes selecting a differentiation order by comparing Augmented Dickey–Fuller results with correlation to the original series: choose the least differencing that meets the stationarity criterion while retaining as much memory as possible. It illustrates the workflow on dollar-bar closing prices and reports an original-series ADF p-value of 0.77 and a selected differentiation order of 0.5, while noting residual drift after transformation.

It also introduces triple-barrier labeling, which assigns long, short, or neutral outcomes when volatility-scaled profit or loss barriers are reached, or when a time limit expires. The example uses a one-day vertical barrier and 1% volatility-based profit and stop levels, producing 1,771 observations across the three classes. Overlapping event labels can make samples dependent, so the tutorial suggests weighting observations by returns and average uniqueness. These choices are strategy-dependent, and stationarity tests or labels alone do not establish predictive power or profitability.

Key ideas

Fractional differentiation can reduce non-stationarity while retaining some time-series memory.
Select the differentiation order by balancing an ADF stationarity criterion against correlation with the original series.
Triple-barrier labeling uses volatility-scaled upper and lower thresholds plus a time limit to define outcomes.
The example labels observations as long, short, or no-trade according to which barrier is reached.
Overlapping labels create sample dependence, which can be addressed by weighting for returns and uniqueness.

Fractional Differencing and Triple-Barrier Labels for Trading Models

Summary

Key ideas

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