![](bg9.png)
stagewise inclusion of regressors in the overall learn-
ing procedure for an ART model (see Section 3) is a
main reason for irrelevant regressors to not pose much
of a problem for our approach.
7 CONCLUSIONS AND FUTURE
WORK
We have presented a spectral splitting method that
improves segmentation in regime-switching time se-
ries, and use the segmentation in the process of cre-
ating a switching regression tree for the regimes in
the model. We have exemplified our approach by
an extension to the ART models–the only type of
models that to our knowledge applies switching trees
in regime-switching models. However, the spectral
splitting method does not rely on specific paramet-
ric assumptions, which allows for our approach to
be readily generalized to a wide range of regime-
switching time-series models that go beyond the limit
of the Gaussian error assumption in the ART mod-
els. Our proposed method is very parsimonious in
the number of split predicates it proposes for candi-
date split nodes in the tree. It only proposes a single
oblique split candidate for the regressors in the model
and possibly a few very targeted time-split candidates,
thus keeping computational complexity of the over-
all algorithm under control. Both types of split can-
didates rely on a spectral clustering, where different
views–phase and trace–on the time-series data give
rise to the two different types of candidates.
Finally, we have given experimental evidence that
our approach, when applied for the exemplifying ART
models, dramatically improves predictive accuracy
over the current approach. Regarding time splits,
we hope to be able to find–and are actively looking
for–real-world time series for future experiments that
will allow us to factor out and compare the quality of
our spectral time-split proposer method to the current
ART approach.
The focus in this paper has been on learning
regime-switching time-series models that will easily
lend themselves to explanatory analysis and interpre-
tation. In future experiments we also plan to evaluate
the potential tradeoff in modularity, interpretability,
and computational efficiency with forecast precision
for our simple learning approach compared to more
complicated approaches that integrates learning of
soft regime switching and the local regimes the mod-
els, such as the learning of Markov-switching (e.g.
Hamilton, 1989, 1990) and gated expert (e.g. Wa-
terhouse and Robinson, 1995; Weigend et al., 1995)
models.
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