  This paper proposes a test for the joint hypothesis of correct dynamic
specification and no omitted latent factors for the Quantile Autoregression. If
the composite null is rejected we proceed to disentangle the cause of
rejection, i.e., dynamic misspecification or an omitted variable. We establish
the asymptotic distribution of the test statistics under fairly weak conditions
and show that factor estimation error is negligible. A Monte Carlo study shows
that the suggested tests have good finite sample properties. Finally, we
undertake an empirical illustration of modelling GDP growth and CPI inflation
in the United Kingdom, where we find evidence that factor augmented models are
correctly specified in contrast with their non-augmented counterparts when it
comes to GDP growth, while also exploring the asymmetric behaviour of the
growth and inflation distributions.
