Quantile Curve Estimation and Visualization for Nonstationary Time Series

There is an increasing interest in studying time-varying quantiles, particularly for environmental processes. For instance, high pollution levels may cause severe respiratory problems, and large precipitation amounts can damage the environment, and have negative impacts on the society. In this article we address the problem of quantile curve estimation for a wide class of nonstationary and/or non-Gaussian processes. We discuss several nonparametric quantile curve estimates, give asymptotic results, and propose a data-driven procedure for the selection of smoothing parameters. This methodology provides a statistically reliable and computationally efficient graphical tool that can be used for the exploration and visualization of the behavior of time-varying quantiles for nonstationary time series. A Monte Carlo simulation study and two applications to ozone time series illustrate our method. R codes with the algorithm for selection of smoothing parameters (described in Section 3) are available in the online supplements.