Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations

Maximum-likelihood estimates of the parameters of stochasticdifferential equations are consistent and asymptotically efficient,but unfortunately difficult to obtain if a closed-form expressionfor the transitional probability density function of the processis not available. As a result, a large number of competing estimationprocedures have been proposed. This article provides a criticalevaluation of the various estimation techniques. Special attentionis given to the ease of implementation and comparative performanceof the procedures when estimating the parameters of the Cox–Ingersoll–Rossand Ornstein–Uhlenbeck equations respectively.