Multifractal detrended cross-correlation analysis for power markets

Multifractal theory has been widely used in kinds of field. In this paper, methods were proposed to study in the power-law auto-correlation and cross-correlation of power operating data based on multifractal detrended analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DXA). We find that both the price and the load time series in California power market and PJM power market exhibit long-term correlation. And the cross-correlation behaviors of the two series in each power market and between the two markets are also analyzed by the method MF-DXA after testing the existence of the cross-correlation of the above power operating data. However, there are some differences in the cross-correlation behaviors between the two markets. It shows that the cross-correlation of the price and the load is significant in every time periods in California 1999 power market, but in the year of 2000 in the same region market, the cross-correlation is insignificant in most time periods. Meanwhile, we conclude that cross-correlation is weaker in the California market than in the PJM market by studying the two consecutive years of the California 1999–2000 and PJM 2001–2002 power markets. We also discuss how the time intervals affect the cross-correlation exponents of the power operating data based on time-delay MF-DXA. An interesting finding is that the biggest cross-correlation exponent of the two series appeared in about 12 days time delay for the PJM 2001 power market and strongest cross-correlation in the California 1999 power market is found in lots of cyclical time intervals.