Detrended fluctuation analysis of short datasets: An application to fetal cardiac data

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 α ) by computing the mean value of the local exponents α L (in the asymptotic regime). The local exponents are obtained as the (numerical) derivative of the logarithm of the fluctuation function F ( s ) with respect to the logarithm of the scale factor s : α L = d log 10 F ( s ) / 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 α L from the averaged fluctuation functions (of all realizations) can minimize the variations in α 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 α and the gestation age.