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 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...

We investigate the finite-sample bias of the quasi-maximum likelihood estimator (QMLE) in spatial autoregressive models with possible exogenous regressors. We derive the approximate bias result of the QMLE in terms of model parameters and also the moments (up to order 4) of the error...