Decay equivalence of intra- and cross-metaorder correlations

Establish whether the autocorrelation of child order signs within a metaorder and the cross-correlation of child order signs between different metaorders decay with lag according to the same functional form and comparable exponent, and quantify this equivalence to assess its role in enabling accurate reconstruction of synthetic metaorders from public trade data.

Background

The paper develops a framework where metaorders of varying sizes and durations produce square-root impact with post-execution decay, and shows that price diffusion requires long-memory cross-correlations between metaorders. Empirical evidence suggests both within-metaorder (intra) and between-metaorder (cross) sign correlations are long-ranged, but their precise relationship is not established.

In the conclusion, the authors put forward a conjecture that the intra- and cross-correlations of child orders decay similarly. Verifying this would help explain why synthetic metaorders can be reconstructed successfully from public data, as reported in related work. Confirming or refuting this equivalence would also sharpen the conditions under which decaying impact remains compatible with diffusive prices.