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

ELC International Meeting on Inference, Computation, and Spin Glasses

Ibuki, Takero^1 ; Higano, Shunsuke^2 ; Suzuki, Sei^3 ; Inoue, Jun-Ichi^4 ; Chakraborti, Anirban^5

Data Mining Group, Service and Solution Development Department, Research and Development Center, 3-6 Hikarino-oka, Yokosuka-shi, Kanagawa 239-8536, Japan^1

Hokkaido Prefectural Police, N2-W7, Chuo-Ku, Sapporo 060-8520, Japan^2

Department of Basic Sciences, Saitama Medical University, 38 Morohongo, Moroyama, Saitama 350-0495, Japan^3

Graduate School of Information Science and Technology, Hokkaido University, N14-W9, Kita-Ku, Sapporo 060-0814, Japan^4

Laboratoire de Mathématiques Appliquées Aux Systèmes, École Centrale Paris, 92290 Chatenay-Malabry, France^5

关键词: Collective behaviour;    Cross correlations;    Multi-dimensional scaling;    Non-stationary time series;    Probabilistic modeling;    Probabilistic models;    Statistical inference;    Theoretical framework;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/473/1/012008/pdf
DOI  :  10.1088/1742-6596/473/1/012008

来源: IOP

【 摘 要 】

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 multidimensional 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.