2018/01/22 by Anirban Chakraborti, Chakraborti, Anirban, Kiran Sharma +9
Economics, Econometrics and Finance · Environmental Science · #Complex Systems and Time Series Analysis #Financial Risk and Volatility Modeling #Ecosystem dynamics and resilience
paper · pdf · doi:10.48550/arxiv.1801.07213
Catastrophic events, though rare, do occur and when they occur, they have\ndevastating effects. It is, therefore, of utmost importance to understand the\ncomplexity of the underlying dynamics and signatures of catastrophic events,\nsuch as market crashes. For deeper understanding, we choose the US and Japanese\nmarkets from 1985 onward, and study the evolution of the cross-correlation\nstructures of stock return matrices and their eigenspectra over different short\ntime-intervals or "epochs". A slight non-linear distortion is applied to the\ncorrelation matrix computed for any epoch, leading to the emerging spectrum of\neigenvalues. The statistical properties of the emerging spectrum display: (i)\nthe shape of the emerging spectrum reflects the market instability, (ii) the\nsmallest eigenvalue may be able to statistically distinguish the nature of a\nmarket turbulence or crisis -- internal instability or external shock, and\n(iii) the time-lagged smallest eigenvalue has a statistically significant\ncorrelation with the mean market cross-correlation. The smallest eigenvalue\nseems to indicate that the financial market has become more turbulent in a\nsimilar way as the mean does. Yet we show features of the smallest eigenvalue\nof the emerging spectrum that distinguish different types of market\ninstabilities related to internal or external causes. Based on the paradigmatic\ncharacter of financial time series for other complex systems, the capacity of\nthe emerging spectrum to understand the nature of instability may be a new\nfeature, which can be broadly applied.\n