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 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...

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...

I derive the finite-sample bias of the conditional Gaussian maximum likelihood estimator in ARMA models when the error follows some unknown nonnormal distribution. The general procedure relies on writing down the score function and its higher-order derivative matrices in terms of quadratic forms...

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...