STATISTICS Review Seminar: Viktor Eriksson

Topic An Extensive Comparison of Small-Sample Properties of Covariance Estimators for MLEs in the Context of ARMA Models

Abstract A common approach for parameter estimation in autoregressive moving-average (ARMA) models is the maximum likelihood estimator (MLE). The inverse Fisher's information matrix (FIM) is consequently an often used estimator for the variance-covariance matrix (VCM) of the MLE. We investigate the small sample properties of five FIM-based estimators for the VCM in a Monte Carlo simulation study. The Box-Jenkins asymptotic estimator and the FIM performed best in respect to the mean squared error (MSE) and relative bias. The observed FIM performed worst in these measures, however it performed best for providing accurate confidence intervals for the ARMA parameters.