Finite sample properties of the maximum likelihood estimator in continuous time models

This dissertation consists of three papers on finite sample properties of the maximum likelihood (ML) estimator of parameters in continuous time dynamic models. In the first chapter, we obtain analytical expressions to approximate the bias and variance of the ML estimator in a univariate model with a known mean. We analyze two cases, when the variable of interest is a stock and when it is a flow. We also study the effect of the initial condition by considering both a fixed and a random initial value. A Monte Carlo study suggests that the performance of the formulae is reasonably good. Analytical bias expressions are then used in the second chapter to compute bias corrected estimators. This chapter also explores other methods for bias reduction that have been employed in the literature, these being the bootstrap, jackknife, and indirect inference. A Monte Carlo experiment shows that all approaches deliver substantial bias reductions. We also explore the robustness of the results to model misspecifications, and provide an empirical application to the broad effective exchange rate series for euro area. The third chapter derives the exact discrete representation corresponding to a cointegrated system of mixed first- and second-order stochastic differential equations with mixed sampling and observable stochastic trends. We also provide some formulae to implement the Gaussian estimation and conduct a Monte Carlo experiment to examine the finite sample properties of the Gaussian estimator. Monte Carlo simulations suggest that the bias and variance of the estimators of the short-run, long-run and adjustment coefficients as well as the variance of the intercepts are mainly determined by the data span, while the bias and variance of the covariance coefficients seem to depend on the sample size.