Multifractal weighted permutation analysis based on Rényi entropy for financial time series

Abstract

Abstract This paper proposes a new method called multifractal weighted permutation analysis based on Renyi entropy (MFWPA) to calculate generalized dimension of financial time series. The generalized dimension obtained by weighted permutation process retains more amplitude information of time series and is closely related to the multifractal properties of the system. The advantages of this method are verified by numerical simulations. We find MFWPA has a less sensitivity to noise and captures the complexity for different parts of sequences by changing the length of sequences. Moreover, we apply this method to investigate multifractal behaviors of different stock indices and compare it with the classical algorithm called standard multifractal analysis based on partition function (SMA). Results show that MFWPA could describe the multifractal behaviors of stock indices in detail and reflect the complexity of time series. In addition, generalized dimensions of shuffled series are larger than the corresponding original series as a consequence of the removed autocorrelation.