Statistical inference of co-movements of stocks during a financial crisis

TL;DR

This paper introduces probabilistic models to analyze and visualize stock co-movements during financial crises, using cross-correlations and a multi-layered Ising model to predict market behaviors.

Contribution

It presents a novel framework combining multi-dimensional scaling and a variant of the Ising model for forecasting social system phenomena in financial markets during crises.

Findings

Stocks cluster tightly during crises as shown by MDS visualization.

The proposed model can predict multiple time-series simultaneously.

Empirical data supports the validity of the models.

Abstract

In order to figure out and to forecast the emergence phenomena of social systems, we propose several probabilistic models for the analysis of financial markets, especially around a crisis. We first attempt to visualize the collective behaviour of markets during a financial crisis through cross-correlations between typical Japanese daily stocks by making use of multi- dimensional scaling. We find that all the two-dimensional points (stocks) shrink into a single small region when a economic crisis takes place. By using the properties of cross-correlations in financial markets especially during a crisis, we next propose a theoretical framework to predict several time-series simultaneously. Our model system is basically described by a variant of the multi-layered Ising model with random fields as non-stationary time series. Hyper-parameters appearing in the probabilistic model are estimated by means of minimizing the 'cumulative error' in the past market history. The justification and validity of our approaches are numerically examined for several empirical data sets.