During periods of market stress, electricity prices can rise dramatically. This paper treats these abnormal episodes or price spikes as count events and attempts to build a model of the spiking process. By contrast to the existing literature, which either ignores temporal dependence in the spiking process or attempts to model the dependence solely in terms of deterministic variables (like seasonal and day of the week effects), this paper argues that persistence in the spiking process is an important factor in building an effective model. A Poisson autoregressive framework is proposed in which price spikes occur as a result of the latent arrival and survival of system stresses. This formulation captures the salient features of the process adequately, and yields forecasts of price spikes that are superior to those obtained from naive models that do not account for persistence in the spiking process.