FUTURE DIRECTIONS 139
and a template is minimized. In this way, one template can match various time
series with varying time. Since the pattern matching–based approaches try to locate
similar patterns among the historical time series, DTW may be directly applied to
locate time-warping patterns. To the best of our knowledge, no existing algorithm
has ever considered the time compression or stretch of market windows. However,
one associated problem with DTW in practice is its expensive time cost (Wang et al.
Second, although the three mean reversion algorithms outperform the previous
algorithms on most datasets, they may fail in certain cases. For example, if the market
contains one stock that drops continuously and signiﬁcantly over some periods, then
all the three algorithms may fail. Such scenarios may simulate a ﬁnancial crisis when
all stocks continuously drop for a certain period, or the case that one stock is hit
by a series of bad news, and its price slashes continuously over a certain period. In
fact, for such cases, most current good-performing algorithms, including Anticor and
all pattern matching–based algorithms, will underperform the naive market strategy.
In our experiments, we choose blue chip stocks, by assuming that they would not
drop continuously for a long period. However, it is always possible that the “black
swan” (Taleb 2008) may exist in the ﬁnancial market and hit your portfolio. Such a
hypothetical market sequence poses a serious challenge: How to achieve a reasonable
performance in such a market?
Third, in Section 9.4, we brieﬂy connect PAMR’s update and the general form
of return-based contrarian strategies. Besides PAMR, we ﬁnd that GP’s update in
Section 4.2 also coincides with the general form of return-based momentum strategies.
This ﬁnding is not abnormal as both adopt similar learning techniques but contrary
trading ideas, that is, contrarian for PAMR and momentum for GP. Based on such
a connection, we can anatomize a portfolio’s expected return and ﬁnd its sources of
proﬁt. Although pure trading strategies have been anatomized for a long time, OLPS
algorithms have yet to be anatomized. Such an analysis will help understand the
behaviors of OLPS algorithms, which is largely unknown in current research. The
resulting empirical observations can help validate the analysis, as is done in previous
studies (Lo and MacKinlay 1990; Conrad and Kaul 1998; Lo 2008).
Fourth, as empirically analyzed in Section 13.6 and discussed in Section 14,
differentassetpools are suitable for differentalgorithms.Also, as there exist thousands
of assets in the ﬁnancial markets, it would be more computationally efﬁcient to select
a subset of assets. This poses an open challenge, that is, how to prepare a proper asset
pool for speciﬁc OLPS algorithms. This challenge is similar to the task of feature
selection, and we plan to explore general methods to automatically select effective
subsets of assets.
Finally, although all the proposed algorithms signiﬁcantly outperform the state of
the art, one important aspect missing in current study is their theoretical guarantees.
As discussed in Section 14.3, there exist several explanations and measures to handle
the issue. Nevertheless, the theoretical guarantees, either the universal property or
others, are still missing for the proposed algorithms. In future, we plan to present
some nontrivial theoretical guarantees for the proposed algorithms, such that we can
be more conﬁdent regarding the algorithms’ practical applicability.
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