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Our earlier work [J. Opt. 19. (2017) 0905603] showed that, in contrast to thefour parameters of the traditional Stokes vector description of the statisticsof the partially polarized light, the complete second-order statistics of thenarrow-band polarized wave is characterized by thirteen parameters. Here weanalyze the second-order statistics of the radiation from a randomly rotatingsource of the electromagnetic radiation, and show that it includes a covarianceof the right and left circular polarizations that is not captured by the Stokesvector formalism. We illustrate this finding on a simple example of rotatingquadrupole.

Improper statistics of the radiation from a randomly rotating source