Analysis on Long-term Memory in Petroleum Futures Price Returns and Volatilities

Long-term memory characteristic is a main subject of financial study.Compared to stock market,long memory researches on futures is less.Lots of researches applied rescaled range(R/S)analysis,revised rescaled range and GPH methods to testing the long-term memory in stock market.And the majority of the researches use ARFIMA model to analyze the time series.This paper introduced different kinds of time series models and unit root method to test the stability of time series.With rescaled range(R/S)analysis and GPH methods,we test the long-term memory of the crude petroleum futures in NYMEX market using EVIEWS,MATLAB,OXMETRICS applied software.We conclude that petroleum futures market's return series doesn't exhibit long-term memory or persistence,but the substitute index(absolute return series)of the volatilities exhibit strong long-term memory.And at the same time,we compared the models which will be more appropriate to describe the return series and volatilities,and we can use GARCH(1,1)model to describe the return series.However,A fractional integration model,FIGARCH(1,d,1)performs significantly better than a traditional volatility model,GARCH(1,1),in modeling the substitute index(absolute return series)of petroleum futures price volatility.