Title: Multiscale inference and long-run variance estimation in nonparametric regression with time series errors
Authors: Marina Khismatullina - University of Bonn (Germany) [presenting]
Michael Vogt - University of Bonn (Germany)
Abstract: New multiscale methods to test qualitative hypotheses about the trend function in the nonparametric regression model with time series errors are developed. Practitioners are often interested in whether the trend has certain shape properties. For example, they would like to know whether it is constant or increasing/decreasing in certain time regions. Our multiscale methods allow us to test for such shape properties of the trend. In order to perform these tests, we require an estimator of the long-run error variance. We propose a new difference-based estimator of it for the case that the errors follow a general AR(p) process. In the technical part, we derive asymptotic theory for the proposed multiscale tests and the estimator of the long-run error variance. The theory is complemented by a simulation study and an empirical application to climate data.