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Detrended fluctuation analysis of short datasets: An application to fetal cardiac data. (English) Zbl 1106.62120
Summary: Using detrended fluctuation analysis (DFA) we perform scaling analysis of short datasets of length 500–1500 data points. We quantify the long range correlation (exponent $\alpha \right)$ by computing the mean value of the local exponents ${\alpha }_{L}$ (in the asymptotic regime). The local exponents are obtained as the (numerical) derivative of the logarithm of the fluctuation function $F\left(s\right)$ with respect to the logarithm of the scale factor $s:{\alpha }_{L}=d{log}_{10}F\left(s\right)/d{log}_{10}s$. These local exponents display huge variations and complicate the correct quantification of the underlying correlations. We propose the use of the phase randomized surrogate (PRS), which preserves the long range correlations of the original data, to minimize the variations in the local exponents. Using the numerically generated uncorrelated and long range correlated data we show that performing DFA on several realizations of PRS and estimating ${\alpha }_{L}$ from the averaged fluctuation functions (of all realizations) can minimize the variations in ${\alpha }_{L}$. The application of this approach to the fetal cardiac data (RR intervals) is discussed and we show that there is a statistically significant correlation between $\alpha$ and the gestation age.
##### MSC:
 62P10 Applications of statistics to biology and medical sciences 62-07 Data analysis (statistics) 62M99 Inference from stochastic processes