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Multifractal Detrended Fluctuation Analysis of Fuel Oil Futures Markets

CHEN Hongtao1,2 (1. Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052, China; 2 .Institute of Energy Soft Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)  
By breaking the traditional concept of financial integral dimensions, the fractal market theory (FMT) can examine the nonlinearity of the financial system on the basis of dynamics and geometry theories by introducing the concept of fractional dimensions. FMT has become an efficient tool to analyze price fluctuations in the financial market. Based on the multifractal theory, the author utilized the multifractal detrended fluctuation analysis (MF-DFA) method to examine the fluctuation of fuel oil futures prices in Shanghai Futures Exchange (SHFE) and Singapore Exchange (SGX). The MF-DFA, which takes the mean of the fluctuation of each sub-series as the statistical point, determines the generalized Hurst exponents based on the power-law of the fluctuation function. The MF-DFA method, which measures the fluctuation singularity of time series, is considered an efficient method of testing the multifractality in the noisy and non-stationary series. Results show that the two fuel oil futures markets present the multifractal characteristics, and the Hurst index of the Shanghai futures market is larger than that of the Singapore futures market. Without following the random walk, the fuel oil futures market is not an effective market, but a typical multifractal market. For the generalized Hurst exponents, the author took 0.5 as the critical point. When the order q is smaller than zero for the returns series of Singapore and Shanghai fuel oil price, the generalized Hurst exponents are larger than 0.5. The small fluctuations of prices are magnified, and display the persistent (or long-range correlated) behavior, highlighting the effects of internal factors of the futures market. For large positive values of q, the generalized Hurst exponents are smaller than 0.5. The large fluctuations of prices are magnified, and display the anti-persistent behavior (or the property of mean-reversion), highlighting the effects of external factors of futures market. When the order q is larger than -5, for each constant value of q, the generalized Hurst exponent for returns series of the Singapore fuel prices is larger than that for Shanghai. This implies that correlations for the returns series of the Singapore fuel prices are higher than those for Shanghai, i.e., the effects of external financial factors of Singapore market on the fluctuations are magnified; the effects of history events on the futures prices are more significant. When the order q is smaller than -5, the situations are contrary to those for q-5. In addition, the model also demonstrates the multifractal spectrum of the Shanghai futures market is wider than that of the Singapore futures market, implying that a single scale cannot be used to describe the dimension of prices fluctuation.
【Fund】: 国家自然科学基金项目(编号:70873058);; 上海市科技发展基金软科学研究项目(编号:10692102900)
【CateGory Index】: F224;F713.35;F764.1
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