  In most prediction and estimation situations, scientists consider various
statistical models for the same problem, and naturally want to select amongst
the best. Hansen et al. (2011) provide a powerful solution to this problem by
the so-called model confidence set, a subset of the original set of available
models that contains the best models with a given level of confidence.
Importantly, model confidence sets respect the underlying selection uncertainty
by being flexible in size. However, they presuppose a fixed sample size which
stands in contrast to the fact that model selection and forecast evaluation are
inherently sequential tasks where we successively collect new data and where
the decision to continue or conclude a study may depend on the previous
outcomes. In this article, we extend model confidence sets sequentially over
time by relying on sequential testing methods. Recently, e-processes and
confidence sequences have been introduced as new, safe methods for assessing
statistical evidence. Sequential model confidence sets allow to continuously
monitor the models' performances and come with time-uniform, nonasymptotic
coverage guarantees.
