Fractal Analysis of Stock Index and Electrocardiograph

We use the modified inverse random midpoint displacement (mIRMD) method to calculate the fractal dimensions of time sequences of arbitrary length. We show that monofractals, crossover-fractals, and the superposition of a fractal, with either a differentiable or periodic function, can be easily identified from the results calculated by the mIRMD. We compare our method with the method of detrended fluctuation analysis (DFA) and point out their differences. We apply our method to real financial and physiological data by considering the movement of the S&P 500 stock index and the electrocardiograph of a patient with ventricular fibrillation