Nonparametric methods for forecasting the Cox process

A Cox process is a Poisson process whose parameter is itself a stochastic process. Current methods used to estimate the underlying intensity process, such as principal component analysis, Markov chain Monte Carlo methods, and maximum likelihood estimation, are limited by memory requirements and computational times to small problems. We introduce a computationally efficient, nonparametric estimation method, REX (Reversed Exponential Smoothing) that allows for the analysis of much larger problems. We report the results of a factorial experiment to test the accuracy of these methods when the underlying intensity is generated by a higher-order autoregressive process. We assess accuracy using Kullback-Liebler Divergence[1].