Abstract
By now the problem of estimating statistical characteristics of red-noise processes is not completely developed. However this problem is of considerable importance for statistical climatology because in the recent years extensive literature has been published containing empirical spectra of red-noise type having noticeable regions of a monotonic increase when a time-scale T increases (with a frequency ω decrease). Such spectra are commonly approximated by the functions increasing like ω-2α, 0 < α < 1 / 2 (red-noise spectra). When dealing with a problem of estimating statistical characteristics of red-noise processes, the estimate errors are to be calculated. As a rule estimate errors become acceptable small when the empirical time series is long enough and asymptotic formulas for the errors can be used. In this paper, we give a list of formulas describing asymptotic behavior of the estimate errors for mean values, covariances, trend parameters, and structure functions for a wide interval of values of α.
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