The Relation Between Conditionally Heteroskedastic Factor Models amd Factor GARCH Models.

The factor GARCH model of Engle (1987) and the latent factor ARCH model of Diebold and Nerlove (1989) have become rather popular multivariate volatility parameterizations due to their parsimony, and the commonality in volatility movements across different financial series. Nevertheless, there is some confusion in the literature between them. The purpose of this note is to make clear their similarities and differences by providing a formal nesting of the two models, which can be exploited to analyze their statistical features in a more general context. At the same time, their differences may be important in the interpretation of empirical results.