  An algorithm is presented to update the multi-fractal spectrum of a time
series in constant time when new data arrives. The discrete wavelet transform
(DWT) of the time series is first updated for the new data value. This is done
optimally in terms of sharing previous computations, in O(L) constant time,
with L the number of levels of decomposition. The multi-fractal spectrum is
then updated also in constant-time. New pre-computation techniques are
presented to further accelerate this process. All possible 2^L data alignments
are taken into account in the course of the incremental updates. The resulting
spectrum estimate is more stable, compared to the current DWT method using only
one dyadic frame, as precise, and more efficient. It is adapted for real-time
on-line updates of the time series.
