Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models

We suggest quantile regression methods for a class of smooth coefficient time series models. We use both local polynomial and local constant fitting schemes to estimate the smooth coefficients in a quantile framework. We establish the asymptotic properties of both the local polynomial and local constant estimators for α-mixing time series. We also suggest a bandwidth selector based on the nonparametric version of the Akaike information criterion, along with a consistent estimate of the asymptotic covariance matrix. We evaluate the asymptotic behaviors of the estimators at boundaries and compare the local polynomial quantile estimator and the local constant estimator. A simulation study is carried out to illustrate the performance of estimates. An empirical application of the model to real data further demonstrates the potential of the proposed modeling procedures.