The Effect Of Filters And Data Lose On Cross-correlation In Time Series

For a multiple-component system, it is necessary to consider the relations between different influence factors. One of the properties to reflect this relation is cross-correlation. When probing the dynamical properties of complex systems, such as physical and physiological systems, the output signal may be not the expected one. It is often a linear or nonlinear filter (or a transformation) of the right one represented the properties we want to investigate. Besides, while data collecting, one often meets a difficulty that the data are incomplete due to natural factors or human factors. Therefore, the prerequisite for analyzing the origin signal is to know which effect the signal with data lose has on the origin one.Here, we investigate what effect kinds of linear and nonlinear filters have on the cross-correlation properties of monofractal series and binomial multifractal series relatively. We use the multifractal detrended cross-correlation analysis (MFDCCA) that has been known well for its accurate quantization of cross-correlations between two time series. We study the effect of five filters:(ⅰ) linear (yi=axi+b);(ⅱ) polynomial (yi=axib);(ⅲ) logarithmic (yi=log(xi+δ));(ⅳ) exponential (yi=exp(axi+b));(ⅴ) power-law (yi=(xi+a)b). We find that for both monofractal and multifractal signals, linear filters have no effect on the cross-correlation properties while the influence of polynomial, logarithmic and power-law filters mainly depends on (a) the strength of cross-correlations in the original series,(b) the parameter b of the polynomial filter,(c) the offset8in the logarithmic filter,(d) both the parameter a and b of the power-law filter. In addition, the parameter a and b of the exponential filter change the cross-correlation properties of monofractal signal, yet they have little influence on that of multifractal signal.Besides, we analyze the effect of two types and two degrees of data lose on traffic data in reality, and Dow Jones Indexes, Hang Seng Index, Shanghai A Index and Shanghai B Index in financial market. Cross-correlation of traffic data with periodicity and regularity has no change even when the proportion of consequent data lose becomes90%. While random data lose affects cross-correlation depending on the proportion of data lose. However, for the long period and mutative financial data, the effect of data lose is more significant. Not only the consequent data lose but random data lose changes the origin cross-correlation and the behavior of scaling. The degree of effect relies on the correlation of origin series and the proportions of data lose.