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

Cai, Zongwu; Xu, Xiaoping

J. Am. Stat. Assoc. 103, No. 484, 1595-1608 (2008).

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.

MSC:

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

Keywords:

bandwidth selection; boundary effect; covariance estimation; kernel smoothing method; nonlinear time series; quantile regression; value-at-risk; varying coefficients

Software:

FinTS