Manifestation of crossover from RMT fluctuation to Poisson fluctuation in BSE sensex, a prototype of financial systems

Abstract

We use the nearest neighbour spacing distribution (NNSD) of random matrix theory (RMT) as a tool to identify the type of spectral fluctuations of matrix ensemble constructed using high frequency BSE sensex values. NNSD shows Wigner distribution for ensemble formed with detrended index values. The detrended raw index values has the universal properties of the Gaussian orthogonal ensemble of random matrices. In contrast, NNSD shows Poisson distribution for ensemble formed using log transformed return of the index values which is corroborated by computation of the number variance. We have also shown the intermediate transitions connecting RMT and Poissonian fluctuations applying NNSD on the data sets generated using power transformation on the return index values. Log transformation is obtained in the asymptotic limit of the power transformation. This gradual changes in the spectral fluctuations from RMT to Poissonian type is reminiscent of localization theory results obtained in simulated experiments. On the contrary, the BSE Sensex values, approximately 2 million data for a period of 2006–2010, has been taken as a prototype of real systems representing an emerging economy of the world.