  We investigate the problem of discovering and modeling regime shifts in an
ecosystem comprising multiple time series known as co-evolving time series.
Regime shifts refer to the changing behaviors exhibited by series at different
time intervals. Learning these changing behaviors is a key step toward time
series forecasting. While advances have been made, existing methods suffer from
one or more of the following shortcomings: (1) failure to take relationships
between time series into consideration for discovering regimes in multiple time
series; (2) lack of an effective approach that models time-dependent behaviors
exhibited by series; (3) difficulties in handling data discontinuities which
may be informative. Most of the existing methods are unable to handle all of
these three issues in a unified framework. This, therefore, motivates our
effort to devise a principled approach for modeling interactions and
time-dependency in co-evolving time series. Specifically, we model an ecosystem
of multiple time series by summarizing the heavy ensemble of time series into a
lighter and more meaningful structure called a \textit{mapping grid}. By using
the mapping grid, our model first learns time series behavioral dependencies
through a dynamic network representation, then learns the regime transition
mechanism via a full time-dependent Cox regression model. The originality of
our approach lies in modeling interactions between time series in regime
identification and in modeling time-dependent regime transition probabilities,
usually assumed to be static in existing work.
