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Many natural phenomena can be described by power-laws. A closer look at various experimental data reveals more or less significant deviations from a 1/f spectrum. We exemplify such cases with phenomena offered by molecular biology, cell biophysics, and cognitive psychology. Some of these cases can be described by first order autoregressive (AR) models or by higher order AR models which are short range correlation models. The calculations are checked against astrophysical data which were fitted to a an AR model by a different method. We found that our fitting method of the data give similar results for the astrhophysical data and therefore applied the method for examples mentioned above. Our results show that such phenomena can be described by first or higher order of AR models. Therefore such examples are described by short range correlation properties while they can be easily confounded with long range correlation phenomena., Comment: 17 pages, 13 figures