  The power spectral density of an observable quantifies the amount of
fluctuations at a given frequency and can reveal the influence of different
timescales on the observable's dynamics. Here, we show that the spectral
density in a continuous-time Markov process can be both lower and upper bounded
by an expression involving two constants that depend on the observable and the
properties of the system. In equilibrium, we identify these constants with the
low- and high-frequency limit of the spectral density, respectively; thus, the
spectrum at arbitrary frequency is bounded by the short- and long-time behavior
of the observable. Out of equilibrium, on the other hand, the constants can no
longer be identified with the limiting behavior of the spectrum, allowing for
peaks that correspond to oscillations in the dynamics. We show that the height
of these peaks is related to dissipation, allowing to infer the degree to which
the system is out of equilibrium from the measured spectrum.
