Amortized Neural Filtering for Calibrated Posteriors in Statistical Arbitrage

Statistical arbitrage trades on an estimate of the state of a residual spread, and conventional practice discards the uncertainty of that estimate. We keep the uncertainty and use it in the trading decision. A Neural Filter Estimator (NFE) is trained on simulated paths of a mean-reverting process whose innovation law is selected by testing candidates against real residuals; once trained, it returns the posterior over the latent state of every spread in a cross-section in one forward pass. Three results follow. On simulated paths with known truth, every practical estimator, ours included, falls in one narrow band of accuracy well below an estimator given full information, so the posterior gains no accuracy over a point estimate; its contribution is a correct account of its own uncertainty. On Korean equities, net of costs, the conventional point estimate forecasts about a thousand basis points per holding period more than it realizes, and the amortized methods cut that gap by a factor of roughly two to eight. Sizing positions from the posterior on the same learned factors as the end-to-end Attention Factor Model matches the Sharpe ratio of those factors under the base rule within the period's noise, at no more risk.