In this paper we develop a parameter estimation procedure for a stochastic process when that process is non-stationary. Although the estimation procedure itself is very general, we derive the model for the particular case of a Poisson process with parameter µ(t) subject to exponential decay. We then illustrate the application of this particular model to a fundamental problem in the management of inventories subject to obsolescence, i.e. how to identify excess inventories in sufficient time to ensure that stocks are cleared before the end of the season.