Many natural phenomena can be described by power-laws of temporal or spatial correlations. The equivalence in frequency domain is the 1/f spectrum. A closer look at various experimental data reveals more or less significant deviations from a 1/f characteristic. Such deviations are especially evident at low frequencies and less evident at high frequencies where spectra are very noisy. We exemplify such cases with four different types of phenomena offered by molecular biology (series of coding sequence lengths from microbial genomes, series of the atomic mobility of the protein main chain), cell biophysics (flickering of red blood cells), cognitive psychology (mentally generated series of apparent random numbers) and astrophysics (the X-ray flux variability of a galaxy). All these examples appear to be described by autoregressive models of the first-order AR(1) or higher-order models. This further shows that a spectrum needs to be first subjected to averaging as, long ago, suggested by Mandelbrot otherwise the spectra can be more or less easily confused and/or approximated by power-laws.