Asymmetric multiscale multifractal detrended cross-correlation analysis for the 1999–2000 California electricity market

In order to access the asymmetric cross-correlation between two time series in a wide range of scales, the method of asymmetric multiscale multifractal detrended cross-correlation analysis (A-MMFCCA) is proposed in this study, which is an extension of the asymmetric detrended fluctuation analysis and the multifractal cross-correlation analysis. Multiscale multifractal detrended cross-correlation analysis enables us to find that the price and the load series of California electricity market exhibit long-range persistent multifractal cross-correlation at different scale ranges during 1999–2000, and the scale range has an important impact on the fractal properties of cross-correlation. Furthermore, the asymmetric cross-correlation between the price and the load series is detected by means of our proposed A-MMFCCA method. Through comparing the local Hurst surfaces with the uptrends and downtrends, we further find that the asymmetric cross-correlation between the price and the load series in 2000 is more significant than that in 1999; the contribution of asymmetric cross-correlation in 1999–2000 mainly depends on different directional trends at different scale ranges. The findings help to interpret the power crisis phenomenon and develop effective and prospective market policy recommendations.