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

We show that the combined use of correlation dimension ( D 2 ) and correlation entropy ( K 2 ) 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 D 2 and K 2 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 D 2 of data and surrogates, K 2 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.