Predictive quantile regression with persistent covariates: IVX-QR approach

Abstract

This paper develops econometric methods for inference and prediction in quantile regression (QR) allowing for persistent predictors. Conventional QR econometric techniques lose their validity when predictors are highly persistent. I adopt and extend a methodology called IVX …ltering (Magdalinos and Phillips, 2009) that is designed to handle predictor variables with various degrees of persistence. The proposed IVX-QR methods correct the distortion arising from persistent multivariate predictors while preserving discriminatory power. Simulations con…rm that IVX-QR methods inherit the robust properties of QR. These methods are employed to examine the predictability of US stock returns at various quantile levels.

The role of economic uncertainty in forecasting exchange rate returns and realized volatility: Evidence from quantile predictive regressions

“…However, Lee (2016) argues that conventional QR econometric techniques are not valid when regressors are highly persistent. Lee (2016) developed quantile econometric methods for robust inference in the presence of persistent and endogenous regressors.…”

“…Lee (2016) suggests that it is convenient to transform Model 2 to remove the intercept term: The specification in Equation 5 is designed to handle predictor variables with various degrees of persistence, since it captures four categories of regressor's persistence: stationary, mildly integrated, local to unity and unit root, and mildly explosive.…”

“…Further, Lee (2016) adopts the IVX filtering of Magdalinos and Phillips (2009). This is analogous to the demeaning process in a predictive mean regression.…”

“…Lee (2016) proposed new IVX-QR estimation methods that are based on the use of IVX filtered instruments. The parameters δ ∈ (0, 1) and c Z <0 are specified by the researcher.…”

“…Krol (2014) is the only study that analyzes the contemporaneous effect of domestic and US uncertainties separately, on the volatility of 10 dollar-based nominal exchange rates of industrialized and developing countries, based on linear regressions. For our purpose, we rely not only on standard linear predictive regressions but also on the quantiles-based model of Lee (2016), which controls for endogeneity and persistence of the predictorcharacteristics we statistically show to exist for the EPU differentials. 1 As can be seen from the above discussion, all the studies dealing with uncertainty and exchange rate movements are in-sample-based analyses.…”