combinatorial_purged_cv¶

Defined in fynance.data

combinatorial_purged_cv(T, n_groups=6, n_test_groups=2, purge=0, embargo=0)[source]

Generate combinatorial purged cross-validation (CPCV) folds.

A single walk-forward path (or a plain purged K-fold) gives exactly one out-of-sample (OOS) performance estimate, so its variance from the particular split chosen is never measured – a lucky or unlucky path looks identical to a robust one. CPCV instead splits [0, T) into n_groups contiguous groups and, for every combination of n_test_groups groups held out as test, purges/embargoes the remainder and yields it as one train/test fold. That produces n_splits = math.comb(n_groups, n_test_groups) folds – versus the single path of walk_forward – whose paths can be reassembled into many distinct OOS return series, turning one backtest into a distribution of OOS Sharpe ratios (and letting one estimate the probability of backtest overfitting, PBO).

Parameters:

Tint: Number of observations.
n_groupsint, optional: Number of contiguous groups to split [0, T) into (sizes as equal as possible; any remainder bars go to the first groups, i.e. the same convention as numpy.array_split). Default 6.
n_test_groupsint, optional: Number of groups held out as test in each fold. Default 2.
purgeint, optional: Number of bars removed from train on both sides of every test group’s boundary (immediately before its start and immediately after its end), so that no train observation straddles a test boundary. Default 0.
embargoint, optional: Number of bars additionally removed from train immediately after each test group’s end (beyond purge), to absorb serial correlation that would otherwise leak test information forward into a subsequent train block. Default 0.

Yields:

(train_idx, test_idx)tuple of numpy.ndarray: Sorted, unique int64 index arrays, same convention as walk_forward. test_idx is the union of the chosen test groups; train_idx is every other index minus the purge/embargo windows.

Raises:

ValueError: If n_test_groups is not strictly between 0 and n_groups, or if n_groups exceeds T (a group would then be empty).

See also

train_test_split, walk_forward

Notes

Combinations are generated in the deterministic order of itertools.combinations applied to range(n_groups). By a standard counting argument, each of the n_groups groups appears in the test set of exactly math.comb(n_groups - 1, n_test_groups - 1) of the math.comb(n_groups, n_test_groups) folds.

References

[1]

Lopez de Prado, M. (2018). Advances in Financial Machine Learning. Wiley. Chapter 7, “Cross-Validation in Finance”.

Examples

>>> import math
>>> folds = list(combinatorial_purged_cv(12, n_groups=4, n_test_groups=1, purge=1))
>>> len(folds) == math.comb(4, 1)
True
>>> train_idx, test_idx = folds[0]
>>> test_idx
array([0, 1, 2])
>>> train_idx  # bar 3 purged (1 bar after the test group's end)
array([ 4,  5,  6,  7,  8,  9, 10, 11])