时间序列数字滤波后自由度的确定——应用于日长变化与南方涛动指数的相关分析

The Determination of Degrees of Freedom for Digital Filtered Time Series——An Application in the Correlation Analysis between Length of Day Variation and SOI

原始观测时间序列进行数字滤波后,其自由度将大大降低。对各种数字滤波器都可以通过 Monte Carlo方法模拟获得对应置信水平的相关系数临界值,从而得到时间序列滤波后的自由度。如果滤波后的频段宽度与Nyquist频率之比为Z,那么对于理想的单边和双边滤波器,时间序列滤波后的自由度为原始值的Z/2和Z倍,非理想滤波器一般不符合此规律。

The degree of Freedom (DOF) of digital filtered time series will be decreased rapidly. To determine the DOF of a filtered data series by different kinds of filters, Monte Carlo method can be applied and the critical correlation coefficients at different confidential levels can be simulated correctly. Assuming that the ratio between filtered frequency band and Nyquist frequency band is Z, the DOF of the filtered data series is Z and Z/2 times as that of its origin data series respectively, for a one-way and a two-way perfect filter. But for a non-perfect filter, this rule is not suitable.