Estimation of Trends Using Ordinary Differential Equations: An Application to Occupational Injuries

In this paper, we present and discuss the dynamic time varying version of trend estimation. These models often underlie the analytical functions that are used in practice by actuaries and economists. We also show how one of the most frequently used softwares (the SAS systems) by practitioners and researchers can be used to fit the dynamics to data. An alternate formulation of the Ordinary Least Squares (OLS) is also given. Using this technique, we analyze occupational injury and illness data from 12 countries. The results for most countries have shown an average decline.