The Determination of Degrees of Freedom for Digital Filtered Time Series——An Application in the Correlation Analysis between Length of Day Variation and SOI
Hua Yan, Minghao Zhong, Yesen Zhu · Acta Astronomica Sinica · 2003
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.