1.6 Feature Engineering & Target Labeling

Basic Prerequisites: Probability & Measure Theory and Python/pandas. Fluency with Pillar 1 - Quantitative Research helps but is not required. (these are the folder-level prerequisites for pages 02–06; page 01 states its own, smaller, entry requirements)

1. Intuition & Practical Objective

Financial machine learning fails for two reasons long before the model is at fault: the features are not stationary enough and the labels are not what the strategy actually does. The first is a feature-engineering problem; the second is a labeling problem. Both are decisions made before any model is fit, and both silently cap the achievable Sharpe.

The standard textbook recipe - “predict the return over the next $h$ bars” - is wrong in a specific, measurable way. A trader does not hold blindly for $h$ bars: they take profit, cut losses, and time out. The Triple-Barrier Method (López de Prado, 2018) labels each observation by which barrier the price path touches first, which is exactly what the P&L of the strategy would have been. And because price levels are non-stationary while returns throw away all memory, Fractional Differentiation finds the minimal $d^{\ast }$ that passes a stationarity test while keeping as much of the price’s long memory as possible.

This folder is the topic-hub for feature engineering & target labeling in Kwant-Atlas. It (a) gives the fast formula/decision lookup below - job #1 of a hub - and (b) routes you to six sub-pages that walk from raw intuition through feature construction, target labeling, the triple-barrier/meta-labeling machinery, the failure modes, and the advanced tooling.

The one-sentence essence. “Label the observation by the first barrier the path touches (not by a fixed-horizon sign), separate direction from bet size with meta-labeling, and difference prices just enough to be stationary without erasing memory - because in finance the target and the features are modelling decisions, not data.”

2. Mathematical Ground Truth & Derivations

Quick-Reference Lookup (job #1). Notation: $P_t$ price, $X_t$ raw feature series, $r_t=\ln (P_t/P_{t-1})$ log-return, ${\sigma }_t$ an ex-ante (point-in-time) volatility estimate, $h$ the vertical-barrier horizon (bars), $pt,sl$ the upper/lower barrier multipliers, $t_{i,0}/t_{i,1}$ the event start / first-barrier-touch times, $c_t$ the number of labels concurrent at $t$, $B$ the backshift operator. All formulas below were re-executed and reproduced numerically (see §3).

Critical caveat (López de Prado §3.4, §19.6). The barriers must use an ex-ante volatility estimate (available at $t_{i,0}$). Using a full-sample or forward-looking $\sigma$ injects the future into the label - see 05 · Failure Modes. Likewise, the right-hand side of every feature row must be computable from data $\le t$; the label may look forward (that is its job), the features may not.

3. Computational Implementation - the labeling engine

This runs on the standard library only and reproduces the verified numbers above: the fractional-differentiation order search with a Dickey–Fuller statistic, the triple-barrier labels, and the concurrency/average-uniqueness computation.

Read the output as the folder’s two punchlines in numbers: the price level needs only $d^{\ast }=0.3$ differencing to become stationary (not $d=1$, which destroys memory), and the 1,450 overlapping triple-barrier labels behave like only 407.6 independent outcomes - the IID assumption overstates the sample by 3.6×.

4. Failure Modes & First-Principles Breakdowns

Hub signposts - the folder’s failure-mode analysis lives in 05 · Failure Modes & Practice. In one line each:

1. Look-ahead in labeling - barriers computed from a future-wide or full-sample $\sigma$ encode information the model cannot legally have at entry.
2. Label overlap / non-IID draws - overlapping event windows make consecutive labels share returns, so naive $k$-fold CV leaks and the effective sample is far smaller than the raw count.
3. Over-differencing - $d=1$ returns are stationary but memoryless; integer differencing (and detrending) removes the cointegrating, slow-moving alpha that the features were supposed to carry.
4. Target leakage through features - any feature row built with data $>t$ (centred z-scores, future normalization, revised fundamentals) is a controlled experiment in fooling yourself.
5. Class imbalance & rare labels - triple-barrier labels can be heavily skewed; accuracy is a misleading metric and rare classes should sometimes be dropped entirely (LdP §3.9).

5. References

• López de Prado, Marcos: Advances in Financial Machine Learning (Wiley, 2018)
• Hastie, Tibshirani & Friedman: The Elements of Statistical Learning (2nd ed., 2009)
• Tsay, Ruey S.: Analysis of Financial Time Series (3rd ed., 2010)
• Hosking, J.R.M. (1981): Fractional differencing, Biometrika 68(1)
• Gu, Kelly & Xiu (2020): Empirical Asset Pricing via Machine Learning, RFS 33(5)

6. Connected Graph Bridges

• Foundational base: Probability & Measure Theory · stationarity & unit-root testing
• Sibling topics: Backtesting Hygiene (triple-barrier labels set the purge/embargo width) · Stat-Arb & Pairs · Fundamental Multi-Factor Models
• Cross-pillar: Tree-Based Factor Ranking & Purged CV (consumes these labels) · Financial ML Pitfalls & Low SNR
• Sub-pages (in-folder): 01 From Zero · 02 Feature Construction · 03 Target Labeling · 04 Triple-Barrier & Meta-Labeling · 05 Failure Modes · 06 Advanced Extensions

Beginner: start at 01 · Practitioner: start at 05