The statistics of polarization in electromagnetic waves or target vector has been studied deeply, generally using Stokes parameters. Unfortunately, all the data-processing includes the assumption that the sampling data are independent of time, without a consideration of the time coherence of the polarization data, such as instantaneous Stokes parameters. In this paper, the definitions of the instantaneous coherent polarization function and polarimetric spectrum are presented for the first time, which shows the coherences of the instantaneous Stokes parameters in both time and frequency domain, even in spatial coherence. The new formula of definition can be extended to spatial propagation coherence, both in free space or any linear medium.