In this note it is shown that the expectation of the usual MLE estimator of the mean-reversion parameter in linear diffusion models does not exist. However, the moment does exist conditionally on the estimator of the autoregressive parameter in the discretized model being positive.

We propose a new semiparametric autoregressive duration (SACD) model, which incorporates the parametric and nonparametric estimators of the conditional duration in a multiplicative way. Asymptotic properties for this combined estimator are presented. The empirical application to the transaction...