A basic goodness-of-fit process fro VARMA (p,q) models

This Working Paper presents some preliminary results for a new goodness-of- t method for VARMA(p,q) models. Relations between least squares residuals and true errors are re-examined, and a new family of statistics is proposed. A new goodness-of- t process is also suggested, that can be seen as an extension of a previously proposed technique in Ubierna and Velilla (2007). The limit behavior of this last random object is obtained as a consequence of a collection of asymptotic results that generalize those obtained previously in Hosking (1981) and Ubierna and Velilla (2007).