Draft:Purged Cross-Validation

Purged and Embargoed Cross-Validation is a time-series-aware model validation technique designed to address information leakage in financial machine learning. It is especially applicable when labels span time intervals rather than individual points in time. The method modifies standard k-fold cross-validation by incorporating two critical mechanisms: purging and embargoing.

Motivation

Traditional cross-validation assumes independent and identically distributed (i.i.d.) observations, which is violated in financial time series. In many financial labeling schemes, each observation represents an event with a starting time and an ending time (e.g., a position held over several days). If a model is trained on data whose label intervals overlap with those in the test set, then future information is inadvertently included in training—this is known as look-ahead bias or information leakage.

Purged cross-validation was introduced ensure that the training set is uncontaminated by test information.

Purging

Purging removes from the training set any observation whose label end time overlaps with the start of the test set. To handle overlapping labels in financial time series, the following notation is used:

• t1: A pandas.Series that maps each observation to the end time of its label.
• [i, j): The index range of the test set in a given fold.
• t0: The start time of the test set, i.e., the timestamp at index i.
• test_max: The latest end time reached by any label in the test set, defined as max(t1[k]) for k in [i, j).

To prevent information leakage, training samples must satisfy:

t1[k] ≤ t0   OR   k > index.searchsorted(test_max) + embargo

This ensures two things:

1. No training label ends after the test set starts (purging).
2. No training sample falls within an embargo period after the test set ends.

Embargoing

Embargoing addresses a more subtle form of leakage: even if an observation does not directly overlap the test set, it may still be affected by test events due to market reaction lag or downstream dependencies. To guard against this, a percentage-based embargo is imposed after each test fold. For example, with a 5% embargo and 1000 observations, the 50 observations following each test fold are excluded from training.

Example

To illustrate the effect of purging and embargoing, consider the figures below. Both diagrams show the structure of 5-fold cross-validation over a 20-day period. In each row, blue squares indicate training samples and red squares denote test samples. Each label is defined based on the value of the next two observations, hence creating an overlap. If this overlap is left untreated, test set information leaks into the train set.

Standard K-Fold Cross-Validation: test samples are randomly partitioned with no attention to label overlap or time ordering. This can lead to contamination of the training set with future information.

Purged K-Fold Cross-Validation: training samples that overlap with the test label horizon are removed. Embargoing is applied to prevent leakage from immediately adjacent samples.

The second figure applies the CPCV procedure. Notice how purging removes overlapping observations from the training set and the embargo widens the gap between test and training data. This approach ensures that the evaluation more closely resembles a true out-of-sample test and reduces the risk of backtest overfitting.

Comparison to Standard K-Fold

Feature	Standard K-Fold	Purged & Embargoed CV
Assumes i.i.d.	Yes	No
Handles overlapping labels	No	Yes
Prevents information leakage	No	Yes
Suitable for financial time series	Poorly	Well

Applications

Purged and embargoed cross-validation is especially useful in:

• Backtesting of trading strategies
• Validation of classifiers on labeled event-driven returns
• Any machine learning task with overlapping label horizons

See also

• Cross-validation (statistics)
• Sharpe ratio
• Backtesting
• Information leakage
• Machine learning in finance

References

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Categories:

• Machine learning
• Investment management