Assess whether finite-spectrum memory improves liquidity modeling

Determine whether the additional multi-timescale generalized Langevin structure improves the description of latent-liquidity dynamics relative to simpler liquidity models, using numerical comparison and empirical testing.

Background

The paper models latent liquidity with a generalized Langevin equation whose intrinsic and order-flow memory kernels are finite sums of exponentials. This introduces several relaxation scales and allows an exact finite-dimensional Markovian lift, but the paper explicitly notes that the empirical or numerical benefit of this additional structure over simpler specifications has not been established.

The unresolved issue is whether the richer memory representation provides a substantively better description of liquidity dynamics, rather than merely a more flexible model formulation. The paper identifies numerical comparison and empirical testing as the means by which this question should be evaluated.