After a major event affecting the world economy, oil prices tend to fluctuate due to the event in the next few months or even years. It can be seen that oil prices may have long-term correlation. In the processing of time series, the traditional ARMA model cannot accurately describe long memory, which leads to the deviation of parameter estimation during the modeling process. In order to better describe the long memory in the time series, this paper establishes the ARFIMA model to perform fractional difference on the series, and obtains the series satisfying the zero-mean ARMA process, then estimates the parameters. Further research shows that the Caputo fractional difference process is a specialized Grunwald-Letnikov (G-L) fractional differential process. Therefore, this paper introduces the Caputo fractional L1 formula into the time series model, and constructs a new fractional difference method to deal with Brent futures price return rate and perform ARFIMA modeling. This method works better in predicting than the traditional ARMA model and the G-L differential ARFIMA model. It can provide more effective assessments in economic markets such as oil price risk measurement and control, helping investors to better avoid market risks and obtain greater returns.
Keywords Oil price, Long memory, Caputo fractional difference, ARFIMA model