Conditioning VAR dynamics on recent returns to capture latent liquidity and concave, mean-reverting impact

Determine whether explicitly conditioning the Vector Autoregression (VAR) transition matrix for binned microstructure modes on recent price changes—so as to encode asymmetric latent liquidity—enables the model to reproduce the empirically observed concave, mean-reverting price impact of metaorders on EuroStoxx futures data.

Background

In their VAR framework calibrated on binned order flow and returns, the authors simulate the impact of exogenous metaorders. The resulting impact is nearly linear and exhibits only mild decay after the metaorder ends, in contrast with empirical findings that show concave (often square-root-like) impact and strong mean-reversion.

To explain this discrepancy, the authors hypothesize that the model lacks an explicit mechanism reflecting how recent price changes reshape the latent liquidity on the order book (asymmetric latent liquidity). They propose conditioning the VAR transition dynamics on recent returns to capture these effects and potentially recover the stylized concave, mean-reverting impact.