  There is increasing evidence that global warming manifests itself in more
frequent warm days and that heat waves will become more frequent. Presently, a
formal definition of a heat wave is not agreed upon in the literature. To avoid
this debate, we consider extreme heat events, which, at a given location, are
well-defined as a run of consecutive days above an associated local threshold.
Characteristics of EHEs are of primary interest, such as incidence and
duration, as well as the magnitude of the average exceedance and maximum
exceedance above the threshold during the EHE.
  Using approximately 60-year time series of daily maximum temperature data
collected at 18 locations in a given region, we propose a spatio-temporal model
to study the characteristics of EHEs over time. The model enables prediction of
the behavior of EHE characteristics at unobserved locations within the region.
Specifically, our approach employs a two-state space-time model for EHEs with
local thresholds where one state defines above threshold daily maximum
temperatures and the other below threshold temperatures. We show that our model
is able to recover the EHE characteristics of interest and outperforms a
corresponding autoregressive model that ignores thresholds based on
out-of-sample prediction.
