基于SSA的时间序列交叉相关分析中指数趋势的去除

Removal the effect of exponential trends in cross-correlation analysis of time series based on singular spectrum analysis

去趋势交叉相关分析是考察非平稳时间序列的长程交叉相关性的一种标度指数.在对含趋势信号的时间序列进行交叉相关分析时,标度会出现交叉点,从而影响相关性分析.针对时间序列中常见的指数型趋势,提出一种采用奇异谱分析法去除该类趋势后再进行交叉相关分析的算法,消除了标度指数图中的交叉点,使得分析结果更为准确.采用二元分数求和滑动平均模型产生两个交叉相关时间序列并叠加指数趋势进行仿真实验,结果表明,奇异谱分析法可以有效地去除指数型趋势,求得的交叉相关标度指数与原始时间序列的标度指数几乎完全吻合,具有较高的精度.

Detrended cross-correlation analysis（DCCA）is a scale index representing the long-range cross-correlation properties between two non-stationary time series.When the time series contain trend signals,the scaling results obtained from the DCCA method appear crossovers,thus affecting the cross-correlation analysis.In this paper,a trend removal algorithm based on singular spectrum analysis（SSA）is proposed to minimize the effect of exponential trends and distortion in the scaling results obtained by the DCCA.To demonstrate the utility of the proposed method,two time series which are the superposition of the exponential trends with the cross-correlated time series generated by the autoregressive fractionally integrated moving average process were used in the simulation.The results show that the exponential trends are removed effectively by the method of SSA and one can accurately quantity the scaling of cross-correlation between two non-stationary time series.