Statistical Properties of Fluctuations: A Method to Check Market Behavior

TL;DR

This paper investigates the statistical and fractal properties of the Bombay stock exchange index over 12 years, using wavelet and spectral analysis to understand market fluctuations and behaviors.

Contribution

It introduces a wavelet-based fluctuation analysis method to characterize non-statistical and fractal features in stock market data.

Findings

Returns exhibit fat-tail distributions.

Presence of weak non-statistical behavior.

Identification of periodic and correlation structures.

Abstract

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.