  The Detrending Moving Average (DMA) algorithm has been widely used in its
several variants for characterizing long-range correlations of random signals
and sets (one-dimensional sequences or high-dimensional arrays) either over
time or space. In this paper, mainly based on analytical arguments, the scaling
performances of the centered DMA, including higher-order ones, are investigated
by means of a continuous time approximation and a frequency response approach.
Our results are also confirmed by numerical tests. The study is carried out for
higher-order DMA operating with moving average polynomials of different degree.
In particular, detrending power degree, frequency response, asymptotic scaling,
upper limit of the detectable scaling exponent and finite scale range behavior
will be discussed.
