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Title: Partially linear quantile regression model with time-varying loadings Authors:  Alev Atak - City University London (United Kingdom) [presenting]
Gabriel Montes-Rojas - Universidad de Buenos Aires (Argentina)
Yonghui Zhang - Renmin University of China (China)
Jose Olmo - University of Southampton (United Kingdom)
Abstract: A semiparametric quantile regression model with factor-augmented predictors and time-varying factor loadings is developed. We propose a two-stage procedure. In the first step, we estimate factors from the mean regression model using a local version of the principal component method and we construct an average quantile regression. In the second step, we obtain partially linear varying coefficient quantile regression using the estimated factors derived in the first step. The proposed method extracts and combines distributional information across different probability masses. Uniform consistency and weak convergence of the estimated quantile factor loading processes are established under general assumptions. We evaluate the volatility-return relationship in real-time applications by observing the behavior of time-varying factor loadings in lower, mid and upper quantiles. We find strong evidence of heterogeneity in dynamic responses.