From Time to Topology: A Comparative Review of Statistical Rigor and Relational Memory in Graph-Based Financial Forecasting

Abstract

This paper discusses how the concept of financial forecasting changes. He compared the “linear lag operator” of traditional econometrics with the new concept of “graph-based learning”. Traditional methods are very strict with statistics, but books and articles say that they do not see the “nonlinear dependence” of the high-frequency market well. On the other hand, “Connectionist” models can predict well, but we don’t know much about their structures. By creating a “topological bridge” with “visibility graph”, this paper puts forward a theoretical concept. In this concept, “market memory” is no longer regarded as the proximity of time, but as “geometric connectivity”. This analysis shows that “GNN” based on visibility structure may provide the advantages of “glass box”. This may help to keep the interpretable artificial intelligence (XAI) robust in the face of change (instability). This paper concludes that it is a necessary theoretical development to turn to “topology” representation. This is crucial for promoting a sovereign and independent financial system.