Abstract
This thesis deals with the estimation and forecasting of factor-augmented quantile autoregressive models. In Chapter 1, we propose a test for the joint hypothesis of correct dynamic specification and no omitted latent factor for the quantile autoregression (QAR). 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 simulation shows that the suggested tests have good finite sample properties. We then examine GDP growth and CPI inflation in the United Kingdom and find that quantile autoregressive models for GDP growth should include latent factors to summarise multiple macroeconomic variables. Such latent factors have non uniform effects on different quantiles of the GDP growth distribution. However, these latent factors do not carry relevant information for modelling the CPI inflation rate distribution.
In Chapter 2, we consider out-of-sample forecasts of the GDP growth and CPI inflation distributions of the United Kingdom with factor-augmented quantile autoregressions under a model averaging framework. We investigate model combinations using weights that minimise the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), the Quantile Regression Information Criterion (QRIC) as well as the leave-one-out cross-validation criterion. We apply the aforementioned methods and find that, on average, for GDP growth, in terms of coverage and final prediction error, equal weights or the weights obtained by the AIC and BIC perform equally well, but are outperformed by the QRIC and the Jackknife approach for the majority of the quantiles of interest. In contrast, the naive QAR(1) model of inflation outperforms all model averaging methodologies.