Improved methods for power spectrum modelling of red noise

We discuss techniques of modelling the power spectrum of variability in cases where the spectral power is continuous but diverges strongly to low frequencies (so-called red noise), as is seen, for example, in the erratic variability of active galaxies and X-ray binaries. First we review the sampling properties of the periodogram and traditional smoothed periodogram estimates of the power spectral density function. Such estimates are biased, are of unknown variance, and have a strongly non-Gaussian distribution, and so are inappropriate for a least-squares goodness-of-fit test. We suggest a new method based on grouping estimates of the logarithm of spectral power density