摘要：
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.
关键词：
power markets, statistical analysis, time series
摘要：
In order to detect and quantify asymmetry of two time series, a novel cross-correlation coefficient is proposed based on recent asymmetric detrended cross-correlation analysis (A-DXA), which we called A-DXA coefficient. The A-DXA coefficient, as an important extension of DXA coefficient rho(DXA), contains two directional asymmetric cross-correlated indexes, describing upwards and downwards asymmetric cross-correlations, respectively. By using the information of directional covariance function of two time series and directional variance function of each series itself instead of power-law between the covariance function and time scale, the proposed A-DXA coefficient can well detect asymmetry between the two series no matter whether the cross-correlation is significant or not. By means of the proposed A-DXA coefficient conducted over the asymmetry for California electricity market, we found that the asymmetry between the prices and loads is not significant for daily average data in 1999 yr market (before electricity crisis) but extremely significant for those in 2000 yr market (during the crisis). To further uncover the difference of asymmetry between the years 1999 and 2000, a modified H statistic (MH) and DMH statistic are proposed. One of the present contributions is that the high MH values calculated for hourly data exist in majority months in 2000 market. Another important conclusion is that the cross-correlation with downwards dominates over the whole 1999 yr in contrast to the cross-correlation with upwards dominates over the 2000 yr. (C) 2016 Author(s).
