Combined use of correlation dimension and entropy as discriminating measures for time series analysis

Abstract

We show that the combined use of correlation dimension (D2) and correlation entropy (K2) as discriminating measures can extract a more accurate information regarding the different types of noise present in a time series data. For this, we make use of an algorithmic approach for computing D2 and K2 proposed by us recently [Harikrishnan KP, Misra R, Ambika G, Kembhavi AK. Physica D 2006;215:137; Harikrishnan KP, Ambika G, Misra R. Mod Phys Lett B 2007;21:129; Harikrishnan KP, Misra R, Ambika G. Pramana – J Phys, in press], which is a modification of the standard Grassberger–Proccacia scheme. While the presence of white noise can be easily identified by computing D2 of data and surrogates, K2 is a better discriminating measure to detect colored noise in the data. Analysis of time series from a real world system involving both white and colored noise is presented as evidence. To our knowledge, this is the first time that such a combined analysis is undertaken on a real world data.