Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models
Zongwu Cai, Xiaoping Xu
Journal of the American Statistical Association December 2008, Vol. 103, No. 484
#002094 20131014 (published)
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.
Keywords: Bandwidth selection; Boundary effect; Covariance estimation; Kernel smoothing method; Nonlinear time series; Quantile regression; Value-at-risk; Varying coefficients.

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