  Time series analysis is quickly proceeding towards long and complex tasks. In
recent years, fast approximate algorithms for discord search have been proposed
in order to compensate for the increasing size of the time series. It is more
interesting, however, to find quick exact solutions. In this research, we
improved HOT SAX by exploiting two main ideas: the warm-up process, and the
similarity between sequences close in time. The resulting algorithm, called HOT
SAX Time (HST), has been validated with real and synthetic time series, and
successfully compared with HOT SAX, RRA, SCAMP, and DADD. The complexity of a
discord search has been evaluated with a new indicator, the cost per sequence
(cps), which allows one to compare searches on time series of different
lengths. Numerical evidence suggests that two conditions are involved in
determining the complexity of a discord search in a non-trivial way: the length
of the discords, and the noise/signal ratio. In the case of complex searches,
HST can be more than 100 times faster than HOT SAX, thus being at the forefront
of the exact discord search.
