Are Returns of Copper Futures in London Metal Exchange Chaotic and Long-Memory? An Empirical Analysis with Close Returns Test

The volatility of returns in financial market is complex, which is often considered as a sort of nonlinear stochastic process or even chaotic process, but little attention has been paid to survey the price behavior in future market. Trying to describe the nature of return behavior correctly is one of the most important tasks in financial engineering and application, which is the basis of financial modeling, risk management, asset pricing and so on. In this paper we apply a new test, close returns test, to detect chaotic phenomenon of return of copper futures in London metal exchange. The results prove that the return series of three-month copper futures is weakly chaotic and exists complicated nonlinear dependence relationship, therefore for the long term modeling the return variation as a linear process (linear regression) or nonlinear process (GARCH, stochastic volatility) in econometrics may be improper to some degree. To explain and embrace the chaotic characteristic is a big challenge of financial modeling in future. We also use rescaled range (R/S) analysis to find the return of copper futures is positively persistent nonlinear process and present typical long memory effect