Research Methodology

Triple-Barrier Labeling (AFML §3)

Standard fixed-horizon returns create noisy labels because they ignore the path taken by prices. The triple-barrier method assigns labels based on which of three barriers is touched first:

                  ┌─── Upper barrier (profit-take): entry × (1 + pt × σ)
                  │
    Price ───────►├─── Vertical barrier (time expiry): t₀ + Δt
                  │
                  └─── Lower barrier (stop-loss):  entry × (1 - sl × σ)

• Upper hit first → +1 (long): price moved up enough to take profit.
• Lower hit first → -1 (short): price moved down past the stop.
• Vertical hit → 0 (no trade): price didn't move enough.

Volatility scaling (§3.1)

Barriers are scaled by local volatility σ computed as the exponentially weighted standard deviation of log returns:

σ_t = EWM_std(ln(p_t / p_{t-1}), span=S)

This makes labels adaptive: the same event in a calm vs. volatile market gets differently-sized barriers.

Meta-labeling (§3.6)

A secondary model predicts whether the primary model's direction was correct (binary: 0 or 1), rather than predicting direction itself. This separates the "when to trade" question from "which direction", and allows the meta-model to focus on sizing and filtering.

Sample Weights (AFML §4)

Labels with overlapping time windows share information. If label A spans bars 10–20 and label B spans bars 15–25, training on both gives redundant signal. The sample weighting scheme:

1. Concurrency (§4.2): Count how many label windows overlap each bar.
2. Uniqueness: Each event's weight is inversely proportional to the average concurrency over its window.
3. Return-weighted (§4.4): Scale by absolute return over the window — large moves are more informative.
4. Time decay (§4.10): Optionally down-weight older samples.

Purged K-Fold Cross-Validation (AFML §7.4)

Standard k-fold CV leaks information in financial data because labels have overlapping time windows that span across folds:

  Fold 1 (train)    │ Fold 2 (test)     │ Fold 3 (train)
  ─────────────────►│──────────────────►│────────────────►
       ┌──── Label A ────┐                      Time →
             Window spans into test fold!

PurgedKFold fixes this by:

1. Purging: Any training sample whose label window [t₀, t₁] overlaps the test fold's time range is removed from training.
2. Embargo: An additional buffer of pct_embargo × N samples after each test fold is also excluded, guarding against serial correlation in residuals.

sklearn CV traps this code avoids

Trap	Standard KFold	PurgedKFold
Label leakage via overlapping windows	Yes — labels spanning fold boundaries leak test info	Purged — overlapping samples removed
Serial correlation after test fold	Yes — adjacent bars are correlated	Embargo period excludes post-test samples
Non-IID assumption	Assumes IID samples	Accounts for temporal dependence
Survivorship bias in time series	Shuffles time order	Preserves chronological order
Redundant samples dominating	Equal weight	Pairs with concurrency-based weighting

Combinatorial Purged K-Fold (AFML §12)

Standard purged k-fold produces N backtest paths (one per fold). CPCV generates C(N, k) splits by designating k out of N folds as test in each combination, producing C(N−1, k−1) independent backtest paths.

For the default (N=6, k=2): - 15 splits = C(6, 2) - 5 backtest paths = C(5, 1)

Each path is a complete walk through the data using only out-of-sample predictions. The distribution of path-level Sharpe ratios feeds into the deflated Sharpe ratio test (Bailey & Lopez de Prado, 2014), which adjusts for multiple testing.

Walk-Forward Validation

For non-overlapping features or as a simpler baseline:

• Expanding window: Train on [0, t), test on [t, t+Δ), advance by step. Training set grows over time.
• Rolling window: Train on [t-W, t), test on [t, t+Δ). Fixed-size training window slides forward.

References

• Lopez de Prado, M. (2018). Advances in Financial Machine Learning (AFML)
  • §3: Triple-barrier labeling and meta-labeling
  • §4: Sample weights and concurrency
  • §7.4: Purged k-fold cross-validation
  • §12: Combinatorial purged cross-validation
• Bailey, D. & Lopez de Prado, M. (2014). The Deflated Sharpe Ratio
• Chan, E. (2013). Algorithmic Trading