Residual Diagnostics for TCA Cost Models

A transaction cost analysis (TCA) model predicts implementation shortfall — the gap between the price you wanted and the price you got — as a function of things like order size, participation rate, and volatility. The residual for any trade is simply actual cost minus predicted cost, and a good model's residuals should look like structureless noise, centered near zero with no obvious pattern left. Residual diagnostics means plotting or grouping these residuals against variables the model uses (and some it doesn't) to check for leftover patterns: are residuals consistently positive for large orders, or for trades near the market close, or on a particular venue?

Any such pattern means the model is missing something systematic rather than just facing irreducible noise, and it points directly at what to add or fix — a size-dependent bias suggests a missing nonlinear impact term, while a time-of-day bias suggests missing intraday liquidity seasonality.

If average residuals are near zero for small orders but consistently $400 higher than predicted for orders above 5% of average daily volume, that pattern points to under-modeled market impact at large sizes, not to random noise.