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We study some general properties of accretion disc variability in the contextof stationary random processes. In particular, we are interested inmathematical constraints that can be imposed on the functional form of theFourier power-spectrum density (PSD) that exhibits a multiply broken shape andseveral local maxima. We develop a methodology for determining the regions ofthe model parameter space that can in principle reproduce a PSD shape with agiven number and position of local peaks and breaks of the PSD slope. Given thevast space of possible parameters, it is an important requirement that themethod is fast in estimating the PSD shape for a given parameter set of themodel. We generated and discuss the theoretical PSD profiles of ashot-noise-type random process with exponentially decaying flares. Then wedetermined conditions under which one, two, or more breaks or local maximaoccur in the PSD. We calculated positions of these features and determined thechanging slope of the model PSD. Furthermore, we considered the influence ofthe modulation by the orbital motion for a variability pattern assumed toresult from an orbiting-spot model. We suggest that our general methodology canbe useful in for describing non-monotonic PSD profiles (such as the trend seen,on different scales, in exemplary cases of the high-mass X-ray binary CygnusX-1 and the narrow-line Seyfert galaxy Ark 564). We adopt a model where thesepower spectra are reproduced as a superposition of several Lorentzians withvarying amplitudes in the X-ray-band light curve. Our general approach can helpin constraining the model parameters and in determining which parts of theparameter space are accessible under various circumstances.

Hot-spot model for accretion disc variability as random process - II. Mathematics of the power-spectrum break frequency