  We examine the scaling regime for the detrended fluctuation analysis (DFA) -
the most popular method used to detect the presence of long memory in data and
the fractal structure of time series. First, the scaling range for DFA is
studied for uncorrelated data as a function of length $L$ of time series and
regression line coefficient $R^2$ at various confidence levels. Next, an
analysis of artificial short series with long memory is performed. In both
cases the scaling range $\lambda$ is found to change linearly -- both with $L$
and $R^2$. We show how this dependence can be generalized to a simple unified
model describing the relation $\lambda=\lambda(L, R^2, H)$ where $H$ ($1/2\leq
H \leq 1$) stands for the Hurst exponent of long range autocorrelated data. Our
findings should be useful in all applications of DFA technique, particularly
for instantaneous (local) DFA where enormous number of short time series has to
be examined at once, without possibility for preliminary check of the scaling
range of each series separately.
