Multifractality in China copper futures market

We use MFDFA method in this study to examine the multifractality of China copper futures market from 2006 to 2012 for the Shanghai Futures Exchange (SFE). Results show that China copper futures market displays multifractal scaling behavior. We also find that the copper futures price fluctuation on SFE is intensive. However, the SFE is more likely to have some profit. The results can provide important implications for understanding the nature of China futures market. Introduction The study of finanicial market’s variation rule has already received a great deal of attentions. Much research has been done in nonlinear science and corresponding complexity for the last few years, ranging from soliton to chaos to fractal [1-4]. MFDFA is widely used to analyse long-range autocorrelations and capture the volatility statistical characteristic in different time scale for non-stationary time series.. However, these MFDFA method [5] will cause new pseudo-wave error due to the discontinuity in segmentation join points during the polynomial fitting, which will lead to distortion of the scaling index [6]. In our paper, we propose a S-R-MFDFA method, which uses the continuous overlapping interval segmentation method to replace the non-overlapping interval segmentation method in the R-MFDFA method and can reduce pseudo-wave error significantly.The S-R-MFDFA method is applied to the copper futures return series of Shanghai Futures Exchange (SFE) and London Metal Exchange (LME) for empirical research. We validate the multifractality of copper futures returns in SFE and LME. Additionally, the degree of multifractality and the market risk is analyzed and compared for the two markets. Our approach We use the MFDFA approach for detecting multifractality of time series. For time series { , 1,2, } k x k N = ..., , the MFDFA method can be summarized with the following steps. (1) Construct a new series and calculate: 1 ( ) [ ]( 1, 2, ) i k k y i x x i N = = − =  ..., (1) (2) The new series ( ) y i is divided into t N ( int( / ( 1)) t N N s = − ) non-overlapping subtime series of s sliding window lengths (The overlap length is 1). (3) For each subtime series ( 1,2, 2 ) t v v N = ..., , there is s points for v . We adopt the polynomial regression and obtain local trend function ( ) y v  . (4) We calculate the average variance for each segments.