A new robust inference for predictive quantile regression
Zongwu Cai, Haiqiang Chen, Xiaosai Liao
Journal of Econometrics Volume 234, Issue 1, May 2023, Pages 227-250
2612 20231010 (published) Views:1580
This paper proposes a novel approach to offer a robust inferential theory across all types of persistent regressors in a predictive quantile regression model. We first estimate a quantile regression with an auxiliary regressor, which is generated as a weighted combination of an exogenous random walk process and a bounded transformation of the original regressor. With a similar spirit of rotation in factor analysis, one can then construct a weighted estimator using the estimated coefficients of the original predictor and the auxiliary regressor. Under some mild conditions, it shows that the self-normalized test statistic based on the weighted estimator converges to a standard normal distribution. Our new approach enjoys a good property that it can reach the local power under the optimal rate with nonstationary predictor and for stationary predictor, respectively. More importantly, our approach can be easily used to characterize mixed persistency degrees in multiple regressions. Simulations and empirical studies are provided to demonstrate the effectiveness of the newly proposed approach. The heterogeneous predictability of US stock returns at different quantile levels is reexamined.
JEL-Codes: C32; C52; C58
Keywords: Auxiliary regressor; Embedded endogeneity; Highly persistent predictor; Multiple regression; Predictive quantile regression; Robust; Weighted estimator

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