Quantile-Covariance Three-Pass Regression Filter

We propose a factor model for quantile regression using quantile-covariance(qcov), which will be called the Quantile-Covariance Three-Pass Regression Filter (Qcov3PRF). Inspired by the Three-Pass Regression Filter (3PRF, Kelly and Pruitt, 2015), our method selects the relevant factors from a large set of predictors to forecast the conditional quantile of a target variable. The measure qcov is implied by the first order condition from a univariate linear quantile regression. Our approach differs from the Partial Quantile Regression (PQR, Giglio et al., 2016) as Qcov3PRF successfully allows the estimation of more than one relevant factor using qcov. In particular, qcov permits us to run time series least squares regressions of each regressor on a set of transformations of the variables, indexed for a specific quantile of the forecast target, known as proxies that only depend on the relevant factors. This is not possible to be executed using quantile regressions as regressing each predictor on the proxies refers to the conditional quantile of the predictor and not the quantile corresponding to the target. As a consequence of running a quantile regression of the target or proxy on each predictor, only one factor is recovered with PQR. By capturing the correct number of the relevant factors, the Qcov3PRF forecasts are consistent and asymptotically normal when both time and cross sectional dimensions become large. Our simulations show that Qcov3PRF exhibits good finite sample properties compared to alternative methods. Finally, three applications are presented: forecasting the Industrial Production Growth, forecasting the Real GDP growth, and forecasting the global temperature change index.