28-06-2012, 02:05 PM
Discovery of motifs to forecast outlier occurrence in time series
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Introduction
This work proposes a new strategy to predict the occurrence of
outlying data in time series, as well as providing accurate forecasts
for them. It is worth highlighting that the goal of this methodology
is to forecast their appearance, instead of detecting them in an
already known set of values, which is a common goal in robust statistics
(Maronna et al., 2007). The majority of robust statistical
techniques perform a posteriori detection, that is, they determine
whether a datum is an outlier or not, but once it has already
occurred. However, a comparison with these techniques will be
of the utmost importance in order to evaluate the accuracy of the
proposed metaheuristic.
Related work
This section provides useful and recent references about the
three main topics involved in this paper: Energy time series forecasting,
motifs discovery in temporal data and robust statistical
methods to detect outliers. For the sake of clarity, these topics have
been separated in three different sections.
Energy time series forecasting
The interest of analyzing electricity price time series resides in
the progressive deregulation of electric power markets. Furthermore,
electricity price time series possess certain features that turn
the prediction into a difficult task: non-constant mean/variance
and frequently outlier occurrences. For this reason, electricity-producer
companies want optimized bidding strategies as well as
needing assessment about the risk of trusting forecasts (Plazas
et al., 2005).
Robust statistical methods to detect outliers
The problem of a posteriori outliers detection in time series has
been widely studied in the literature, and faced from many different
points of view. In fact, the existence of even few outliers
usually leads to inaccurate models and not satisfactory forecasts
(Galeano et al., 2006), since they may deeply influence the
estimates that classical methods propose (Carnero et al., 2007).
For this reason, there is a large family of robust statistical
methods (Rousseeuw and Hubert, 2011) that deal with outliers
and, particularly, propose approaches to detect their existence in
the datasets subjected to analysis. Gelper et al.
Fundamentals
This Section first defines some terms in order to prevent possible
misinterpretations in sensitive terms. Since the proposed
methodology is based on an existing algorithm, this Section also
provides a brief summary of the mathematical fundamentals
underlying the PSF algorithm. Note that a more detailed explanation
can be found in Martínez-Álvarez et al. (in press).