Long memory and nonlinear dependence structure in crude oil futures returns and volatility

In order to investigate the nature of international crude oil futures and present evidence of long memory and nonlinear dependence for crude oil futures volatility as well as returns, a certain number of recent statistical tests, such as the powerful BDS test, the fractional integration test and other known statistics, are applied. The results show that though the returns themselves contain little serial correlation, the market volatility series have significant long-term dependence structures which may have important implications for volatility forecasts and derivative pricing. On the other hand, evidence of strong ARCH effect is also presented, and, moreover, the BDS statistics on the standardized residuals of the fitted GARCH model indicate that the ARCH-type process may generally explain the nonlinearities in the data. It seems that the crude oil futures market can be appropriately modeled by ARCH and fractal processes. These findings indicate that it would be beneficial to assess the behavior of the crude oil and price the oil derivative contracts by encompassing long memory and nonlinear structure.