Most practitioners sample financial data at fixed intervals (daily, hourly, weekly), but this choice is a convention, not an engineering decision. Time bars have poor statistical properties: returns are heteroskedastic (high variance at open/close, low at midday), non-IID, and fat-tailed. These properties hurt any downstream model — IC calculations are less reliable, signal standard deviations are poorly estimated, and backtest statistics are inflated.
Two tools from López de Prado (2018) improve the quality of raw signal inputs. First, activity-based sampling (dollar bars or volume bars) synchronises data collection with information arrival, producing returns closer to IID. Second, fractional differentiation resolves the stationarity-memory dilemma: integer differencing achieves stationarity (required for many ML models and IC calculations) but destroys all memory (the very thing that makes a signal predictive). Fractional differencing finds the minimum differencing order that achieves stationarity while preserving as much memory as possible.
Learning objectives. By the end of this note you should be able to:
- describe the four bar types (time, tick, volume, dollar) and explain why dollar bars have better statistical properties;
- state the fractional differentiation operator and its weight sequence;
- identify the minimum differencing order using the ADF test as a function of ;
- apply the FFD method to produce a stationary series with maximum memory retention;
- explain why fractional differentiation does not make integer differentiation obsolete.
In this lesson
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- From time bars to activity-based bars
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- The stationarity-memory dilemma
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- Fractional differentiation
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- The Fixed-Width Window FFD method
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- Application to stat-arb feature engineering
Before you start
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