Multifractal analysis of the WTI crude oil market, US stock market and EPU

Abstract

This paper adopts multifractal methods to analyze the nonlinear correlations among economic policy uncertainty (EPU), the crude oil market and the stock market. First, using multifractal detrended fluctuation analysis (MF-DFA), we find that each of the three series shows multifractality, and the sources of multifractality are all from long-range correlations and fat-tailed distributions. However, for the stock and oil price series, the long-range correlation has a greater impact, while the fat-tailed distribution contributes more to EPU multifractality. Furthermore, we apply multifractal detrended cross-correlation analysis (MF-DCCA) to analyze the cross-correlation multifractal features among the three series. The generalized Hurst exponents of any two series are significantly greater than 0.5, and the stock and oil price series have the strongest cross-correlation values. Coupling detrended fluctuation (CDFA) analysis of the three series shows that the coupling correlation among the three sequences is also multifractal. The chi-squared statistic reveals that the contribution of the stock market to the multifractality of the coupling correlation is greater than that of other series, and EPU has the smallest influence on the coupling correlation. Finally, we employ multiscale multifractal analysis (MMA) to visualize the dynamic behaviors of the correlations among the series. The results show that the cross-correlation of stock with the oil price has some symmetry at small- and large-scale fluctuations. Additionally, the influence of EPU on the overall coupling features is mainly reflected under small-scale fluctuations, and at large scales, the coupling correlation of the three series remains similar to the Hurst surface of stock with the oil price. These results are useful for building predictive models.