Spectral densities describing off-white noises

For the white noise, the spectral density is constant, and the past (restriction to (-∞, 0)) is independent from the future (restriction to (0,+∞)). If the spectral density is not too far from being constant, then dependence between the past and the future can be eliminated by an equivalent measure change. A necessary and sufficient condition for a spectral density to have such a property (in other words, to describe an off-white noise) is derived here from well-known results.