  Previous studies indicate that nonlinear properties of Gaussian time series
with long-range correlations, $u_i$, can be detected and quantified by studying
the correlations in the magnitude series $|u_i|$, i.e., the ``volatility''.
However, the origin for this empirical observation still remains unclear, and
the exact relation between the correlations in $u_i$ and the correlations in
$|u_i|$ is still unknown. Here we find analytical relations between the scaling
exponent of linear series $u_i$ and its magnitude series $|u_i|$. Moreover, we
find that nonlinear time series exhibit stronger (or the same) correlations in
the magnitude time series compared to linear time series with the same
two-point correlations. Based on these results we propose a simple model that
generates multifractal time series by explicitly inserting long range
correlations in the magnitude series; the nonlinear multifractal time series is
generated by multiplying a long-range correlated time series (that represents
the magnitude series) with uncorrelated time series [that represents the sign
series $sgn(u_i)$]. Our results of magnitude series correlations may help to
identify linear and nonlinear processes in experimental records.
