不同滤波方法在去趋势波动分析中去噪的应用比较

研究了连续噪声和尖峰噪声对去趋势波动分析的影响,发现噪声的存在使得双对数曲线在尺度较小时发生了"转折"现象.针对这一问题,文中采用三种不同滤波方法对理想时间序列进行了实验,结果表明,多级Vondrak滤波得到的高频序列与真实噪声序列无论是在强度还是在演变趋势上都展现出惊人的一致性,低频滤波序列的去趋势波动分析结果与真实信号十分接近,多级Vondrak滤波基本上能够消除由于噪声所引起的"转折"现象,而且这一研究结果对于滤波周期阈值的依赖性并不太大.多点滑动加权平均滤波虽然能够在一定程度上减轻噪声对于去趋势波动的影响,但不能从根本上消除由于噪声所引起的"转折"现象.快速傅里叶滤波在选择合适的滤波周期阈值时,能够基本消除噪声对去趋势波动分析的影响,但是由于其滤波结果对于滤波周期阈值的依赖较大,在实际应用中滤波周期阈值的选取比较困难.因此,多级Vondrak滤波是消除噪声对去趋势波动分析结果影响的一种有效的途径.关键词：多级Vondrak滤波去趋势波动分析多点滑动加权平均滤波快速傅里叶滤波

Comparison of applications of different filter methods for de-noising detrended fluctuation analysis

We studied the effects of continuous noises and random spikes on detrended fluctuation analysis, and found that the noises lead to the appearance of crossovers in the double logarithm curves when the linear fitting scale was less than a characteristic scale s_×. To solve this problem, we use three kinds of filter methods, multi-stage Vondrak filter, N-point weighted moving average filter and fast Fourier filter, to filter high frequency from the analyzed time series. The results indicate that the evolution trend and intensity of high frequency series by multi-stage Vondrak filter is almost identical to those of real noises. Further investigation showed that multi-stage Vondrak filter can eliminate the phenomenon of crossover, and the DFA results of lowpass filtering time series are less dependent on the threshold of the filter periods. To some extent, N-points weighted moving average filter can partly eliminate the effect of noises on DFA, but can not completely eliminate the phenomenon of crossover caused by noises. Fast Fourier filter can almost totally eliminate the effect of noises on DFA when the period of filter adopts an appropriate value, but the filtering results have a stronger dependence on the period of filter, so it is difficult to select the period of filter in practical application. Therefore, comparatively speaking, multi-stage Vondrak filter is an effective measure to alleviate the effects of noises on the DFA results.