Learning Undirected Graphs in Financial Markets

TL;DR

This paper explores methods for learning undirected graphical models in financial markets, emphasizing Laplacian constraints that relate to market factors and stock correlations, and proposes algorithms tailored to financial data characteristics.

Contribution

It introduces a novel approach to incorporate Laplacian constraints in graph learning for financial data and develops algorithms addressing non-stationarity and clustering.

Findings

Laplacian constraints have meaningful interpretations in financial contexts.

Proposed algorithms effectively handle stylized facts like non-stationarity.

Guidelines for estimating graphs in financial markets are provided.

Abstract

We investigate the problem of learning undirected graphical models under Laplacian structural constraints from the point of view of financial market data. We show that Laplacian constraints have meaningful physical interpretations related to the market index factor and to the conditional correlations between stocks. Those interpretations lead to a set of guidelines that users should be aware of when estimating graphs in financial markets. In addition, we propose algorithms to learn undirected graphs that account for stylized facts and tasks intrinsic to financial data such as non-stationarity and stock clustering.