What can we learn from the history of gasoline crack spreads?: Long memory, structural breaks and modeling implications

In this paper, we investigate the long-range auto-correlations of crack spreads using a nonparametric method, named detrended moving average (MF-DMA). We find that the auto-correlations display multiscaling behaviors and are dominated by the anti-persistence (mean-reversion) in the long-term. Moreover, the auto-correlations are multifractal, indicating that various small and large fluctuations display different scaling behaviors. Using a technique of rolling windows, we find that some extreme events can drive the degree of anti-persistence and the multifractality (complexity) to rise up. In other words, these events have negative impacts on market efficiency. However, the effects of these events are not alike. We also detect long-range auto-correlations in crack spread volatilities and find a strong persistent behavior and multifractality. Finally, we discuss the modeling implications of the findings on long-range auto-correlated patterns. Our results indicate that ARFIMA-GARCH models can capture the major dynamics of large fluctuations. For small fluctuations, they are misspecified. Interestingly, we find that the strong long-range auto-correlated behaviors do not imply that ARFIMA model which takes long memory into account can outperform random walk model in the sense of out-of-sample prediction. The major reason may be that market complexity exploited in this paper causes the low predictability of ARFIMA model.