  The Hurst exponent $H$ of long range correlated series can be estimated by
means of the Detrending Moving Average (DMA) method. A computational tool
defined within the algorithm is the generalized variance $
\sigma_{DMA}^2={1}/{(N-n)}\sum_i [y(i)-\widetilde{y}_n(i)]^2\:$, with
$\widetilde{y}_n(i)= {1}/{n}\sum_{k}y(i-k)$ the moving average, $n$ the moving
average window and $N$ the dimension of the stochastic series $y(i)$. This
ability relies on the property of $\sigma_{DMA}^2$ to scale as $n^{2H}$. Here,
we analytically show that $\sigma_{DMA}^2$ is equivalent to $C_H n^{2H}$ for
$n\gg 1$ and provide an explicit expression for $C_H$.
