Temporal heterogeneity learning for functional panel quantile regressions

In this paper, we introduce a novel approach to address temporal heterogeneity in functional panel data by proposing a partial functional quantile regression model. The model assumes that the functional parameter changes over unknown time regimes. To estimate the completely time-varying parameter vector, regime-varying functional parameter, and unknown time regimes, we develop a three-step estimation technique. Then, we establish the asymptotic normality of the estimators and demonstrate the consistency of the identification procedure used for detecting unknown time regimes. Finally, we illustrate the competitive performance of the model and its associated statistical inference methods through a simulation study as well as two real applications: the “idiosyncratic volatility puzzle" and air pollution analysis.