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Our VWAP article shipped a static, weekly-refit volume curve and called the forecaster the weakest link. This is the follow-up: a Bayesian intraday updater run against the same 500-parent BTCUSDT harness, with the IS delta conditioned on realized curve error.

Dynamic Mode Decomposition fits a linear operator to nonlinear market dynamics. The only question that matters: do the fitted modes persist from one window to the next, and does the rolling spectral radius lead realised volatility? Here is the measurement protocol and the code to run it.

The blog's standing answer to the accuracy-vs-latency tension is a two-stage fast/slow split. Distillation is a different answer: train one small model to mimic the ensemble. The KD loss, temperature, born-again nets, early exits for a variable latency budget, and the distill-to-FPGA pipeline — plus the measurements that would decide whether it beats the two-stage split.

Selection bias in the search is not the only way a regression fools you. When the regressor is correlated with the error, more data makes the estimate more confidently wrong. Instrumental variables applied to the one endogeneity problem this blog has already left open: permanent impact from net taker flow.

Fitting a self-exciting point process to real crypto trade tape: where the three numbers (mu, alpha, beta) come from, how to estimate the branching ratio n, whether the exponential kernel survives a goodness-of-fit test, and how much n moves when you change the estimation window.

Hamiltonian Neural Networks are provably stable — but stability is worthless if the conserved quantity does not exist. Learning a scalar H via autograd, symplectic integration, and the falsification test that decides whether a financial (q, p) pair is canonical at all.

Granger causality on crypto prices done two ways — differenced returns and Toda-Yamamoto on levels — with a correct Wald implementation, an effective-N corrected causality matrix, and a rolling-stability test of whether the lag is tradeable at all.