Engle and Manganelli (2004) propose CAViaR, a class of models suitable for estimating conditional quantiles in dynamic settings. Engle and Manganelli apply their approach to the estimation of Value at Risk, but this is only one of many possible applications. Here we extend CAViaR models to...

To date, the literature on quantile regression and least absolute deviation regression has assumed either explicitly or implicitly that the conditional quantile regression model is correctly specified. When the model is misspecified, confidence intervals and hypothesis tests based on the...