Quantifying self-similarity in cardiac inter-beat interval time series

We compare and quantify the scaling and long-range persistence (long memory) in time series using five different techniques: power-spectral, wavelet variance, semi-variograms, rescaled-range (R/S) and detrended fluctuation analysis. We apply these techniques to both normal and log-normal synthetic fractional noises and motions generated using the spectral method, where a normally distributed white noise is appropriately filtered such that its power-spectral density, S, depends upon frequency, f, according to S~f^-beta. Finally, we examine the long-range persistence of cardiac interbeat intervals. We find that for normal [N] and log-normal [LN] fractional noises: (1) power-spectral analysis does a reasonably good job at correctly quantifying the strength of long-range persistence for all beta[N] and beta>-0.5[LN]; (2) semivariograms, 1.2<beta<2.5[N and LN]; (3) rescaled range 0.0<beta<0.8[N and LN]; (4) wavelet variance analysis all beta[N] and beta>-0.8[LN]; (5) detrended fluctuation analysis -0.8<beta<2.2[N] and -0.2<beta<2.2[LN]