MGARCH models: Trade-off between feasibility and flexibility

Multivariate GARCH (MGARCH) models need to be restricted so that their estimation is feasible in large systems and so that the covariance stationarity and positive definiteness of conditional covariance matrices are guaranteed. This paper analyzes the limitations of some of the popular restricted parametric MGARCH models that are often used to represent the dynamics observed in real systems of financial returns. These limitations are illustrated using simulated data generated by general VECH models of different dimensions in which volatilities and correlations are interrelated. We show that the restrictions imposed by the BEKK model are very unrealistic, generating potentially misleading forecasts of conditional correlations. On the other hand, models based on the DCC specification provide appropriate forecasts. Alternative estimators of the parameters are important in order to simplify the computations, and do not have implications for the estimates of conditional correlations. The implications of the restrictions imposed by the different specifications of MGARCH models considered are illustrated by forecasting the volatilities and correlations of a five-dimensional system of exchange rate returns.     

Identifying, estimating and testing restricted cointegrated systems: An overview

The notion of cointegration has led to a renewed interest in the identification and estimation of structural relations among economic time series. This paper reviews the different approaches that have been put forward in the literature for identifying cointegrating relationships and imposing (possibly over-identifying) restrictions on them. Next, various algorithms to obtain (approximate) maximum likelihood estimates and likelihood ratio statistics are reviewed, with an emphasis on so-called switching algorithms. The implementation of these algorithms is discussed and illustrated using an empirical example.