Fig 6. Regression of the actual (il-)liquidity against the different (il-)liquidity measures.

Regression of the actual illiquidity ${ℒ}_{OB}^{-1}$ on three same-day illiquidity measures (after rescaling so that the samples means coincide): The direct measure of orders market impact ${ℒ}_{\mathrm{\text{I}}}^{-1}$, the publicly available measure ${ℒ}_{\mathrm{\text{TH}}}^{-1}$ that corresponds to the theoretical and empirical impact, and the well-known Amihud ILLIQ measure [39]. Both ${ℒ}_{\mathrm{\text{I}}}^{-1}$ and ${ℒ}_{\mathrm{\text{TH}}}^{-1}$ outperform ILLIQ (R ² ≈ 0.86 vs. 0.74). Note that a high predictability remains when lagging ${ℒ}_{\mathrm{\text{TH}}}^{-1}$ by one day (R ² ≈ 0.83 vs. 0.71). The regression slopes for the four graphs are, respectively: 0.9, 0.95, 0.87 and 0.93.