Like many customer arrival processes, patient arrivals to the psychiatric ward or the emergency department (ED) exhibit strong cyclic behavior. Inspired by the nascent super-resolution literature, we propose a method for estimating the intensity of a nonhomogeneous Poisson process as a simple sum of sinusoids. The estimator is both interpretable and flexible, and hence suitable for use in modelling as well as in high resolution simulations.
We first discuss some surprising estimation pitfalls that can arise when intuitive heuristics are used. In ordinary time series literature, a computationally intensive semidefinite program is used to address these issues. Remarkably, we show that a pictorial method can achieve stronger theoretical guarantees by making a mild assumption on the amplitudes of the sinusoids. We apply our method to patient arrivals data from an academic ED to determine the extent to which the arrival rate can be represented by simple harmonics.