Analysis of the behaviour of the detrended BSE sensex data

The objective of this work is to investigate the pattern exhibited by detrended intra-day BSE Sensex data for the years 2006 to 2012. The detrended data are analysed using Principal Component Analysis (PCA) and its non-linear version, Kernel Principal Component Analysis (KPCA). The detrended data is found to display a high degree of correlation which indicates that the evolution of the detrended prices is restricted to a very low dimensional subspace of the original vector space in which the analysis is done. Different types of synthetic data are generated, which when subject to the same set of analyses, are found to give results along expected lines, thereby verifying the efficacy of the techniques employed. Hurst coefficients of the detrended data sets are calculated for different years using modified R/S analysis. The Hurst coefficient is also computed for the entire data set by gradually changing the scale of analysis and also by using the sliding window technique. In all cases the data set are found to be persistent in nature thereby reinforcing the conclusions obtained by the PCA/KPCA formalism.