Analysis Of Financial Time Series Based On Multifractal And Complexity

In this paper,we extend and improve several methods of time series research and propose three new methods of time series analysis.Aiming at the financial markets of many countries and regions as research objects,we study the dynamics characteristics of financial time series based on the stock index.First,we propose the weighted multiscale Rényi permutation entropy(MSWRPE)based on the weight assigned to each vector,which could consider the amplitude information and make the analysis of time series complexity more detailed.Secondly,we propose the multifractal weighted permutation analysis model based on Rényi entropy(MFWPA)to calculate generalized dimension of financial time series.MFWPA could describe the multifractal behaviors of time series in detail and reveal the internal structure of time series.At last,we propose k-entropy curves and the K-Fisher(KF)index to study the stability of stock indexes in different countries and regions.The main research contents of the paper are as follow:(1)We propose the weighted multiscale Rényi permutation entropy(MSWRPE)based on the weight assigned to each vector.We first use the metric to simulate Gaussian white noise and ARFIMA sequences,and analyze the effects of various parameters in MSWRPE.Later we also use this metric in the analysis of the actual stock market and try to distinguish the stock index markets in different regions.(2)We propose multifractal weighted permutation analysis model(MFWPA)based on Rényi entropy and use it to calculate the fractal dimension of financial time series.The fractal dimension obtained through the weighted permutation process can retain more time series amplitude information,which is also closely related to the multifractal characteristics of the system.We first analyze the simulation sequence of the three models to explore whether the method can describe the multifractal behavior of the sequence and whether it has strong anti-interference to noise.After that,we use this method to study the multifractal behavior of different stock indexes,and compare it with the standard multifractal analysis based on partition function(SMA).Finally,we also use this method for the shuffled series of each stock index in order to analyze the source of the multifractal of the financial time series of the actual market.(3)We propose the complexity-entropy curves model based on k-entropy and the K-Fisher(KF)index.Our results show that the KF index is a good extension of the traditional Shannon-Fisher(SF)index.We first conducted a simulation analysis through the fractional Brownian motion(fbm),combined with the Hurst exponent to analyze the complexity of fbm.We try to find the relationship between the exponent and complexity,and the extreme point of the complexity-entropy curve.After that,we use this method to analyze financial time series obtained from stock indexes in different regions.We use the complexity-entropy curve and the KF index to analyze the complexity of stock indexes in different regions and try to distinguish them.