Multivariate-ARCH: Bias Evaluation for the ML Estimator

Economics

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p>At the present time, there exists an important and growing econometric literature that deals with the application of multivariate-ARCH models to a variety of economic and financial data. However, the properties of the estimation procedures that are used have not yet been fully explored. In this paper we provide analytical theoretical results concerning the important biases that can arise when the ML estimation method is employed in a simple bivariate structure. We analyse 2 models: one proposed in Wong and Li (1997) (where the disturbances are dependent but uncorrelated) and another proposed by Liu and Polasek (1999, 2000) (where conditional correlation is allowed). We show the evolution of the biases in both models and how they are always larger than those of a univariate framework in the special case that conditional heteroscedasticity is falsely assumed. While in the first model the authors reported very small biases in their simulation study, we find that the biases can be very severe in some of the parameters if the difference between the intercepts in the two variance equations is relatively large. Finally, an empirical application is considered.