Nonparametric quantile estimations for dynamic smooth coefficient models. (English) Zbl 1286.62029

Summary: 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 \(\alpha\)-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.


62G05 Nonparametric estimation
62G08 Nonparametric regression and quantile regression
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)


Full Text: DOI Link