Why asynchronous estimation?
Binance and Kraken do not print trades on a common clock. Hayashi–Yoshida covariance works directly with overlapping observation intervals instead of fabricating a synchronized series.
CASE 01 · MARKET MICROSTRUCTURE
Multi-Scale Lead–Lag
Stable BTC price discovery from Binance to Kraken from ~50 ms to ~1.95 s.
CORE SAMPLE12.6M
Binance BTC observations in April 2026.
LAG GRID50 MS
Main empirical resolution.
FREQUENCY BANDS8 SCALES
Approximately 0.10s to 25.60s.
TEMPORAL AUDIT3 MONTHS
January, February and April 2026.
RESEARCH QUESTION
Price discovery is not necessarily single-scale.
A venue can react first at sub-second horizons yet behave differently at slower adjustment scales. Synchronizing irregular trades can distort the result.
Why multiple scales?
Daubechies wavelet filters decompose lagged covariance into dyadic bands, producing a profile of immediate price discovery and slower cross-venue adjustment.
ESTIMATOR PIPELINE
From raw event time to scale-by-scale lag.
The sign convention and synthetic-shift behavior are validated before any exchange result is interpreted.
Ingest event-time data
Normalize public trades without forcing a shared timestamp grid.
Build lagged HY contrast
Shift the second series over candidate lags and accumulate overlapping return intervals.
Apply wavelet filters
Use Daubechies coefficients and autocorrelation wavelets to isolate dyadic scales.
Estimate each maximum
Select the lag maximizing absolute filtered contrast at every scale and audit stability.
EMPIRICAL EVIDENCE
Stable direction from ~50 ms to ~1.95 s.
Binance leads Kraken across all tested BTC scales in the core sample, while the exact magnitude remains regime-dependent.
White maxima remain on the negative-lag side under the documented ordering, indicating a Binance lead over Kraken.
The direction survives the monthly audit; the precise lag magnitude moves with the sample.
The estimator is challenged outside the headline BTC venue pair.
SIGN CONVENTION
Interpretation is unit-tested.
Series 1 is written first. A negative estimate means series 1 leads series 2; a positive estimate means series 2 leads series 1. Shifted synthetic data is used before interpreting live-market samples.
LIMIT
Dependence is not free arbitrage.
Fees, latency, queue position, market impact and the instability of lag magnitude separate statistical price-discovery evidence from an executable strategy.