Rigorous statistics for asynchronous time series.
Black Quantum is an independent research lab working at the intersection of statistical theory, asynchronous data, and financial markets — from asymptotic proofs to production systems.
Black Quantum is an independent research lab working at the intersection of statistical theory, asynchronous data, and financial markets — from asymptotic proofs to production systems.
Our core programme is inference for high-frequency, asynchronously observed data — a problem where classical statistics breaks down and careful theory pays off in live systems.
Covariance and dependence estimation under asynchronous sampling and microstructure noise, with rigorous asymptotic guarantees carried through to deployable estimators.
Reconstruction and modelling of limit-order-book dynamics from raw order-by-order data; microstructure-aware features for prediction on futures markets.
Neural methods that respect the statistical structure of financial data — regime change, heavy tails, and the ever-present risk of overfitting.
Walk-forward validation, look-ahead detection, and formally verified research pipelines. We treat evaluation methodology as a research problem in its own right.
Almost everything we measure is observed asynchronously — two processes, each recorded at its own irregular times. Ask how they move together and the standard fix is to force both onto a shared clock: interpolate, bin, resample. That single step injects bias — correlations collapse toward zero as sampling tightens (the Epps effect). Finance built rigorous estimators that work natively on asynchronous data, with no synchronization. That machinery has barely left finance. The same structure — and the same broken workarounds — sit at the foundation of field after field.
Ice cores, sediments, and tree rings are sampled at irregular depths — and even the timestamps are uncertain. Correlating two proxies is a known minefield.
Reverberation mapping and multiwavelength time-lags need the covariance of two unevenly sampled light curves from telescopes that observe when they can.
Labs are drawn sporadically, vitals frequently. The coupling between them carries clinical signal — but the sampling is fully asynchronous.
Glucose every five minutes, heart rate every second, motion at 50 Hz. The cross-signal coupling is the product — and it's measured off-clock.
Sequencing destroys the cell, so no cell is seen twice and time itself is reconstructed. Gene–gene dynamics live on a latent, asynchronous clock.
Packets are timestamped, but every machine keeps its own drifting clock. Here the twist inverts: the clock relationship itself is the unknown you must estimate.
Camera, LiDAR, and radar each sample the road at their own rate — no two ever capture the same instant. Fusing them safely means reconciling streams that never line up.
High-frequency covariance under asynchronous ticks — the problem where the rigorous estimators were first built, and our home ground.
Some of these break new ground even for the finance toolkit: uncertain observation times (climate, networked clocks) and a latent, reconstructed clock (single-cell). These are not ports of an existing method — they are open problems, and the focus of our work.
Real data: WTI (CL) and Brent (BZ) crude futures trades on CME, one session (2026-05-15, from Databento market-by-order data). Their correlation measured at 5-minute sampling is ≈0.87 — but sample the same trades on a finer grid (previous-tick) and the estimate collapses: the Epps effect. The second toggle shows a simulated pair where the truth (ρ = 0.80) is known exactly. This is the failure mode our estimators are built to fix. Drag the slider.
Estimators come with proofs, not just backtests. If we can't state the assumptions, we don't trust the result.
Every positive result is treated as a bug until it survives walk-forward testing, leakage audits, and independent replication.
Research isn't finished at the paper. We carry methods through simulation, real data, and production infrastructure.
Where the mathematics matters most, we machine-check it — bringing proof assistants such as Lean into quantitative finance.
Black Quantum was founded by Yang Azzollini, whose doctoral research at the University of Oxford — supervised by Brian Ripley and Peter Clifford — developed correlation methods for asynchronously observed financial data. The lab continues that programme, carrying estimation theory from its asymptotic foundations through to deployed systems.
We're interested in collaborations, consulting on high-frequency statistics and neural-network systems, and conversations with people who care about getting the details right.