  In a sequential regression setting, a decision-maker may be primarily
concerned with whether the future observation will increase or decrease
compared to the current one, rather than the actual value of the future
observation. In this context, we introduce the notion of parity calibration,
which captures the goal of calibrated forecasting for the increase-decrease (or
"parity") event in a timeseries. Parity probabilities can be extracted from a
forecasted distribution for the output, but we show that such a strategy leads
to theoretical unpredictability and poor practical performance. We then observe
that although the original task was regression, parity calibration can be
expressed as binary calibration. Drawing on this connection, we use an online
binary calibration method to achieve parity calibration. We demonstrate the
effectiveness of our approach on real-world case studies in epidemiology,
weather forecasting, and model-based control in nuclear fusion.
