Volume bars vs time bars — return normality
InconclusiveVolume bars vs time bars — return normality
2026-06-06 · status: inconclusive · 4.4s
Hypothesis: Sampling BTC on a volume clock (volume bars) yields log-return distributions closer to i.i.d. Gaussian than fixed 1h time bars: lower excess kurtosis, lower Jarque-Bera, and weaker |return| autocorrelation (vol clustering).
Verdict: CONFIRMED (Randverteilung) — Volume-Bars sind deutlich näher an Gauss: excess kurtosis 63.2→19.9 (+69%), Jarque-Bera 9,310,992→917,791, skew -0.89→+0.02. Das Vol-Clustering blieb dagegen ~gleich (|return|-Autokorr 0.291→0.300) — Volume-Bars normalisieren die Randverteilung, nicht die zeitliche Abhängigkeit. Für z-Score/Std-Annahmen Volume-Bars bevorzugen; Fat Tails bleiben (kurt > 0).
Key metrics
| metric | value |
|---|---|
| n_time_bars | 55,826 |
| n_volume_bars | 55,762 |
| excess_kurt_time | +63.2440 |
| excess_kurt_volume | +19.8750 |
| kurt_reduction_pct | +68.6000 |
| abs_autocorr_time | +0.2914 |
| abs_autocorr_volume | +0.2996 |
| jb_time | 9,310,991.70 |
| jb_volume | 917,791.10 |
Approach
BTC 1m → 1h time bars (55,826) and matched-count volume bars (55,762, ~13,615 volume/bar). Compare log-return distributions. Gaussian reference: excess kurtosis 0, low Jarque-Bera, |return| autocorrelation ≈ 0 (no vol clustering).
Distribution stats
| n | std | excess_kurtosis | skew | jarque_bera | abs_autocorr_lag1 | |
|---|---|---|---|---|---|---|
| time_bars_1h | 55825 | 0.0067 | 63.2435 | -0.8931 | 9.31099e+06 | 0.2914 |
| volume_bars | 55761 | 0.0067 | 19.8752 | 0.0161 | 917791 | 0.2996 |
- Excess kurtosis: 63.24 (time) → 19.88 (volume) — +69% toward Gaussian
- |return| autocorr lag-1: 0.291 → 0.300 — -3% less vol clustering
