  We consider mixed-integer quadratic optimization problems with banded
matrices and indicator variables. These problems arise pervasively in
statistical inference problems with time-series data, where the banded matrix
captures the temporal relationship of the underlying process. In particular,
the problem studied arises in monitoring problems, where the decision-maker
wants to detect changes or anomalies. We propose to solve these problems using
decision diagrams. In particular we show how to exploit the temporal
dependencies to construct diagrams with size polynomial in the number of
decision variables. We also describe how to construct the convex hull of the
set under study from the decision diagrams, and how to deploy the method online
to solve the problems in milliseconds via a shortest path algorithm.
