This paper develops the approximate bias of the ordinary least squares estimator of the mean reversion parameter in continuous-time Lévy processes. Several cases are considered, depending on whether the long-run mean is known or unknown and whether the initial condition is fixed or random. The...

We derive the approximate results for the bias and mean squared error of a large class of estimators to orders O(n^(-5/2)) and O(n^(-3)), respectively, given a sample of n observations.The results are built on a stochastic expansion of the moment condition used to identify the econometric...

We develop the analytical second-order bias of a Value-at-Risk estimator based on an ARCH(1) volatility specification when the parameters are estimated by the method of quasi maximum likelihood. We show that the bias results from two sources: assumption on the distribution of the standardized...