Mateusz Pipień

Bayesian Comparison of Bivariate GARCH Processes. The Role of the Conditional Mean Specification

Abstract We use the official daily PLN/USD and PLN/DEM exchange rates to compare various bivariate ARCH-type models through their Bayes factors, similarly to Osiewalski and Pipien (2004). In the previous paper a pure VAR(1)-VechGARCH(1,1) framework (with no exogenous variable) was assumed. In this chapter we introduce the DEM/USD rate from the FOREX market; it is assumed exogenous. Using the relation (PLN/USD)/(PLN/DEM) ≈ DEM/USD, treated as the cointegration equation, we build a conditional ECM model with competing bivariate GARCH structures for the error process. We also use much longer time series than in the previous work. Bayesian comparison of different GARCH specifications indicates that a simple t -BEKK(1,1) is clearly the best, no matter whether our exogenous variable and the ECM term are included or not. The presence of these important variables in the conditional mean of the bivariate process enormously helps in improving the model fit, but has only small effect on our inference on the conditional covariance matrix.