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A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition
Multi-step ahead forecasting is still an open challenge in time series
forecasting. Several approaches that deal with this complex problem have been
proposed in the literature but an extensive comparison on a large number of
tasks is still missing. This paper aims to fill this gap by reviewing existing
strategies for multi-step ahead forecasting and comparing them in theoretical
and practical terms. To attain such an objective, we performed a large scale
comparison of these different strategies using a large experimental benchmark
(namely the 111 series from the NN5 forecasting competition). In addition, we
considered the effects of deseasonalization, input variable selection, and
forecast combination on these strategies and on multi-step ahead forecasting at
large. The following three findings appear to be consistently supported by the
experimental results: Multiple-Output strategies are the best performing
approaches, deseasonalization leads to uniformly improved forecast accuracy,
and input selection is more effective when performed in conjunction with
deseasonalization
Lazy Model Expansion: Interleaving Grounding with Search
Finding satisfying assignments for the variables involved in a set of
constraints can be cast as a (bounded) model generation problem: search for
(bounded) models of a theory in some logic. The state-of-the-art approach for
bounded model generation for rich knowledge representation languages, like ASP,
FO(.) and Zinc, is ground-and-solve: reduce the theory to a ground or
propositional one and apply a search algorithm to the resulting theory.
An important bottleneck is the blowup of the size of the theory caused by the
reduction phase. Lazily grounding the theory during search is a way to overcome
this bottleneck. We present a theoretical framework and an implementation in
the context of the FO(.) knowledge representation language. Instead of
grounding all parts of a theory, justifications are derived for some parts of
it. Given a partial assignment for the grounded part of the theory and valid
justifications for the formulas of the non-grounded part, the justifications
provide a recipe to construct a complete assignment that satisfies the
non-grounded part. When a justification for a particular formula becomes
invalid during search, a new one is derived; if that fails, the formula is
split in a part to be grounded and a part that can be justified.
The theoretical framework captures existing approaches for tackling the
grounding bottleneck such as lazy clause generation and grounding-on-the-fly,
and presents a generalization of the 2-watched literal scheme. We present an
algorithm for lazy model expansion and integrate it in a model generator for
FO(ID), a language extending first-order logic with inductive definitions. The
algorithm is implemented as part of the state-of-the-art FO(ID) Knowledge-Base
System IDP. Experimental results illustrate the power and generality of the
approach
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