Feature Documentation¶

Comprehensive documentation of all features used for structural break detection.

Feature Categories¶

Statistical Moments

Mean, variance, skewness, kurtosis differences between segments.

Statistical Moments
Effect Sizes

Cohen's d, Glass's delta, Hedges' g for standardized comparisons.

Effect Sizes
Hypothesis Tests

Welch's t-test, Kolmogorov-Smirnov, Mann-Whitney U statistics.

Hypothesis Tests
Distribution Metrics

Wasserstein distance, ECDF distance, overlap coefficient.

Distribution Metrics
Spectral Features

FFT-based features: spectral centroid, bandwidth, entropy.

Spectral Features
Wavelet Features

Multi-resolution decomposition using DWT coefficients.

Wavelet Features

Each time series is split at a potential break point into pre-segment and post-segment:

Pre-segment   |  Post-segment
--------------+---------------
 values[0:T]  |  values[T:end]

Features capture differences between these segments.

Based on XGBoost feature importance analysis:

Rank	Feature	Category	Importance
1	`ks_statistic`	Hypothesis Test	Highest
2	`mean_diff_normalized`	Statistical Moment	Very High
3	`std_ratio`	Statistical Moment	Very High
4	`cohens_d`	Effect Size	High
5	`mann_whitney_u`	Hypothesis Test	High
6	`welch_t_stat`	Hypothesis Test	High
7	`median_diff`	Statistical Moment	Medium

Model	Feature Count	Performance
xgb_core_7features	7	0.6188 AUC
xgb_30f_fast_inference	30	0.6282 AUC
xgb_70_statistical	50 (selected from 70)	0.6685 AUC
xgb_tuned_regularization	70+	0.7423 AUC
gradient_boost_comprehensive	100+	0.7930 AUC
meta_stacking_7models	200 (selected from 339)	0.7662 AUC

Feature-Performance Relationship

Performance generally improves with more features, but with diminishing returns after ~70 features.

Category	Key Features	Best Used For
Statistical Moments	mean_diff, std_ratio	Level shifts, volatility changes
Effect Sizes	cohens_d, hedges_g	Scale-invariant detection
Hypothesis Tests	ks_statistic, welch_t_stat	Statistical significance
Distribution Metrics	wasserstein_distance	Full distributional change
Spectral Features	spectral_centroid	Frequency changes
Wavelet Features	dwt_energy	Multi-scale changes