Efficient importance sampling for ML estimation of SCD models

The evaluation of the likelihood function of the stochastic conditional duration (SCD) model requires to compute an integral that has the dimension of the sample size. ML estimation based on the efficient importance sampling (EIS) method is developed for computing this integral and compared with QML estimation based on the Kalman filter. Based on Monte Carlo experiments, EIS-ML estimation is found to be more precise statistically, but involves an acceptable loss of quickness of computations. The method is illustrated with real data and is shown to be easily applicable to extensions of the SCD model.