arXiv:0905.4237v1 [q-fin.ST] 26 May 2009 Statistical Properties of Fluctuations: A Method to Check Market Behavior Prasanta K. Panigrahi, Sayantan Ghosh, P. Manimaran, Dilip P. Ahalpara 1 Prasanta K. Panigrahi, Indian Institute of Science Education and Research (Kolkata), Salt Lake City, Kolkata 700 106, India and Physical Research Laboratory, Navrangpura, Ahmedabad 380 009, India. ‖∗∗ 2 Sayantan Ghosh, The Insitute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600 113, India. †† 3 P. Manimaran, Center for Mathematical Sciences, C R Rao Advanced Institute of Mathematics, Statistics and Computer Science, HCU campus, Hyderabad 500 046, India. ‡‡ 4 Dilip P. Ahalpara, The Insitute for Plasma Research, Bhat, Gandhinagar, 382 428, India. §§ Summary. We analyze the Bombay stock exchange (BSE) price index over the period of last 12 years. Keeping in mind the large fluctuations in last few years, we carefully find out the transient, non-statistical and locally structured variations. For that purpose, we make use of Daubechies wavelet and characterize the fractal behavior of the returns using a recently developed wavelet based fluctuation analysis method. the returns show a fat-tail distribution as also weak non-statistical behavior. We have also carried out continuous wavelet as well as Fourier power spectral analysis to characterize the periodic nature and correlation properties of the time series. 1 Introduction Financial markets are known to show different behavior at different time scales and under different socio-economic conditions. The random behavior of fluctuations in the smaller time scales and the manifestation of structured behavior at intermediate and long time scales have been well studied [1]-[13]. Many of the stock markets have shown large scale fluctuations during the past three years. Here we concentrate on the behavior of the fluctuation of the Bombay stock exchange (BSE) high price values in daily trading. The point that makes the analysis of the BSE price index interesting is the fact that it has a significant fluctuations on a shorter time scale while growing tremendously over a longer time period. The statistical properties of the fluctuations and the behavior of the returns of such a growing market are of ‖ This paper is dedicated to the memory of Prof. J. C. Parikh, who was one of the founding fathers of econophysics in India. ∗∗ prasanta@prl.res.in †† sayantan@imsc.res.in ‡‡ rpmanimaran@gmail.com §§ dilip@ipr.res.in