  Probability forecasts for binary events play a central role in many
applications. Their quality is commonly assessed with proper scoring rules,
which assign forecasts a numerical score such that a correct forecast achieves
a minimal expected score. In this paper, we construct e-values for testing the
statistical significance of score differences of competing forecasts in
sequential settings. E-values have been proposed as an alternative to p-values
for hypothesis testing, and they can easily be transformed into conservative
p-values by taking the multiplicative inverse. The e-values proposed in this
article are valid in finite samples without any assumptions on the data
generating processes. They also allow optional stopping, so a forecast user may
decide to interrupt evaluation taking into account the available data at any
time and still draw statistically valid inference, which is generally not true
for classical p-value based tests. In a case study on postprocessing of
precipitation forecasts, state-of-the-art forecasts dominance tests and
e-values lead to the same conclusions.
