Order-flow and long-memory in a simulated financial market

<p dir="ltr">This project investigates the origins of long-memory in financial market order-flow by replicating and empirically testing the <a href="http://dx.doi.org/10.1103/PhysRevE.71.066122" rel="noreferrer" target="_blank">Lillo-Mike-Farmer (LMF)</a> model. The model proposes that persistent autocorrelation in trade signs arises from large parent orders that are split into smaller child orders following a power-law size distribution. We successfully reproduced the theoretical behaviour of the model through simulation, confirming that long-memory emerges when metaorder sizes follow a heavy-tailed distribution. Using Johannesburg Stock Exchange (JSE) tick data, we applied the <a href="https://arxiv.org/abs/2503.18199" rel="noreferrer" target="_blank">Maitrier-Loeper-Bouchaud</a> (MLB) algorithm, and developed an adaptive version, to reconstruct synthetic metaorders in the absence of trader identifiers. While the simulated results validated the LMF framework, empirical analysis (based on <a href="http://dx.doi.org/10.1103/PhysRevLett.131.197401" rel="noreferrer" target="_blank">Sato and Kanazawa's</a> methodology) found little evidence of long-memory in JSE order-flow, suggesting possible differences in trader behaviour or market structure. Overall, the project delivered a complete replication of the LMF model, an adaptive MLB extension, and a comprehensive test of the LMF framework on JSE data.</p>