Vol.:(0123456789) SN Computer Science (2021) 2:322 https://doi.org/10.1007/s42979-021-00671-z SN Computer Science ORIGINAL RESEARCH A Statistical Test for Detecting Dependency Breakdown in Financial Markets Siva Rajesh Kasa 1  · Malay Bhattacharyya 2 Received: 28 December 2020 / Accepted: 28 April 2021 / Published online: 5 June 2021 © The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd 2021 Abstract Correlations among stock returns during volatile markets difer substantially as compared to those from quieter markets. Dur- ing times of fnancial crisis, it has been observed that the ‘traditional’ dependencies in global markets break down. However, such an upheaval in the dependency structure happens over a span of several months, with the breakdown coinciding with a major bankruptcy or a sovereign default. An important aspect of risk management is to efectively identify the duration of breakdown and create tailor-made models for these extreme events; nevertheless, there are few statistical methods to identify such signifcant breakdowns. The purpose of this paper is to propose a simple test to detect such structural changes in global markets. This test relies on the assumption that asset price follows a Geometric Brownian Motion. We test for a breakdown in dependence structure using eigenvalue decomposition of the correlation matrix. We derive the asymptotic distribution of the test statistic under the null hypothesis and apply the test to stock returns. We also compute the power of this proposed test and compare it with the power of other existing tests. Through extensive experimentation, we show that the proposed test is able to efectively detect the times of structural breakdown in global stock markets, despite the simplifying assumption of Geometric Brownian Motion of stock prices. Keywords Correlation matrix · Fluctuation test · Local power Introduction Change point detection is a well-known problem in retro- spective analysis of time series data. Traditionally, the prob- lem of change point detection is posed as a hypothesis test- ing problem with the null-hypothesis indicating structural stability in the time series and the alternate indicating one or multiple breakdowns. Change point detection has wide applicability—from study of genes in cancers [17] to detec- tion of fnancial fraud [4] to signal processing [11]. Change point detection is complementary to sequential detection wherein new data are continually arriving and are adaptively analyzed. In this work, we are concerned with the change point detection specifc to fnancial time series. A signifcant amount of prior literature has focused on detecting the changes in the mean [21] and variance of a time series [14]. Another important, often overlooked, problem in statistical modeling of fnancial time series is to analyze and detect structural changes in the relationship among stock returns. The structural dependency among various fnancial time series is modeled using the Pearson correlation matrix. Long-term risk-averse investors tend to hold portfolios of assets whose returns are not positively correlated for diver- sifcation benefts. However, there is compelling empirical evidence that the correlation structure among returns of the assets cannot be assumed to be constant over time, see, e.g. [9, 15, 24] and [23]. In particular, during periods of fnancial crisis, correlations among stock returns increase, a phenom- enon which is sometimes referred to as diversifcation melt- down. Given that duration of fnancial crisis is spread across months/years, our work is motivated by the real-life problem This article is part of the topical collection “Computational Statistics” guest edited by Anish Gupta, Mike Hinchey, Vincenzo Puri, Zeev Zalevsky and Wan Abdul Rahim. * Siva Rajesh Kasa kasa@u.nus.edu Malay Bhattacharyya malay.bhattacharyya@iimkashipur.ac.in 1 School of Computing, National University of Singapore, Singapore, Singapore 2 Indian Institute of Management Kashipur, Kashipur, India