  Improvement in time resolution sometimes introduces short-range random noises
into temporal data sequences. These noises affect the results of power-spectrum
analyses and the Detrended Fluctuation Analysis (DFA). The DFA is one of useful
methods for analyzing long-range correlations in non-stationary sequences. The
effects of noises are discussed based on artificial temporal sequences.
Short-range noises prevent power-spectrum analyses from detecting long-range
correlations. The DFA can extract long-range correlations from noisy time
sequences. The DFA also gives the threshold time length, under which the noises
dominate. For practical analyses, coarse-grained time sequences are shown to
recover long-range correlations.
