Search for the periodicity of the prime Indian and American stock exchange indices using date-compensated discrete Fourier transform

The behaviour of Indian stock markets has a persistent close association with the behaviour of American stock exchange. The present work is an effort in this direction and the purpose of the present work is to investigate the periodicity of the two prime Indian stock market indices viz. SENSEX and NIFTY and the prime American stock market indices viz. DOW-JONES and S&P500. To serve the present purpose we have here used SENSEX logarithmic daily close data during the period from 1st January, 1990 to 31st December, 2013, NIFTY logarithmic daily close data during the period from 3rd July, 1990 to 31st December, 2013, DOW-JONES logarithmic daily close data during the period from 10th January, 1928 to 31st December, 2013 and S&P500 logarithmic daily close data during the period 3rd January, 1950 to 31st December, 2013. For the present analysis we have first used double exponential smoothing on all the four time series in order to remove the trend and next we have generated monthly averages of the smoothed time series in order to remove the irregular fluctuations. At the final stage Ferraz-Mello method of date-compensated discrete Fourier transform (DCDFT) has been applied on the present four double-smoothed monthly averaged time series. Study reveals periods for SENSEX of 11, 53 and 142 months; for NIFTY periods of 22, 38, 52 and 139 months; for DOW-JONES periods of 23, 25, 27, 30, 59, 107, 138, 194 and 494 months and for S&P500 periods of 28, 66, 74, 149 and 384 months. With this specific periodic behaviour we have also observed some pseudo-periods in the present four financial time series which certainly adds to the uncertainty in the process of prediction for the same.