  Periodograms are common tools used to search for periodic signals in unevenly
spaced time series. The significance of periodogram peaks is often assessed
using false alarm probability (FAP), which in most studies assumes uncorrelated
noise and is computed using numerical methods such as bootstrapping or Monte
Carlo. These methods have a high computational cost, especially for low FAP
levels, which are of most interest. We present an analytical estimate of the
FAP of the periodogram in the presence of correlated noise, which is
fundamental to analyze astronomical time series correctly. The analytical
estimate that we derive provides a very good approximation of the FAP at a much
lower cost than numerical methods. We validate our analytical approach by
comparing it with Monte Carlo simulations. Finally, we discuss the sensitivity
of the method to different assumptions in the modeling of the noise.
