Multiscaling Properties of Environmental Related Commodities

Zeyu Zheng, Naoko Sakurai, Takeshi Fujiwara, Kousuke Yoshizawa, Shuhei Miyake, Xiang Gao, Kazuko Yamasaki


For stock, electricity and crude oil futures markets, we study the return intervals t between the daily volatilities of the price changes that above a certain threshold q. We find that for different threshold q, the probability density function)(t P scales with the mean interval Pf t tt t= as ( ) ( / )/ . The scaling function f(x) is similar in form for all three markets. Weekly periodicity is identified for electricity market. We compare the systematic deviations of return intervals’ cumulative distribution from scaling. The results show that some stocks and electricity show very weak systematic deviation, while the other stocks and crude oil show apparent systematic deviation. We support this finding by studying the m-th moment )/( >><=< ttµmm m /1 q. We generate surrogate records using the Schreiber method. We suggest that the multiscaling of NordPool and Crude oil mainly account from finite size and discreteness, and the multiscaling of stocks are account from nonlinear correlations.


Econophysics, Long-Term Memory, Fluctuations, Long Range Correlations

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