Exploring Stationarity and Fractality in Stock Market Time-series

The stock market is known for its volatility and variable nature. It is also observed that various stock market indices behave in tandem with other country, geographical or global indices. The changes that took place in the time series information on average Sensex and composite index of BSE and Nasdaq over a phase ranging from 31 Oct 2007 to 1 Nov 2022 were monitored closely. Daily readings were considered and evaluated. Persistence or anti-persistence behavior of the time series has been studied by application of fractal mathematics. Hurst exponent estimation for BSE and Nasdaq has been performed using two methods, WVA and FVSM, to determine whether the series containing the data are a pure random walk or comprise underlying trends. Unit root tests of ADF and KPSS along with SPWVD have been applied on the time series data set to verify whether the series is nonstationary. The experimental results reveal that both time series exhibit nonstationary and anti-persistent behavior.