Consistent Specification Test of the Quantile Autoregression

TL;DR

This paper introduces a new test for the correctness of quantile autoregression models, capable of identifying whether issues stem from dynamic misspecification or omitted factors, with demonstrated good finite sample performance and practical application to UK economic data.

Contribution

It develops a novel joint hypothesis test for quantile autoregression models that accounts for latent factors and provides a method to identify the source of model misspecification.

Findings

Factor-augmented models are correctly specified for UK GDP growth.

Non-augmented models are inadequate for GDP growth.

The proposed tests show good finite sample properties.

Abstract

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.