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Title: Multiscale inference for nonparametric time trends Authors:  Marina Khismatullina - University of Bonn (Germany)
Michael Vogt - University of Bonn (Germany) [presenting]
Abstract: New multiscale methods are developed to test qualitative hypotheses about the regression function $m$ in a nonparametric regression model with fixed design points and time series errors. In time series applications, $m$ represents a nonparametric time trend. Practitioners are often interested in whether the trend $m$ has certain shape properties. For example, they would like to know whether $m$ is increasing/decreasing in certain time intervals. The multiscale methods allow us to test for such shape properties of the trend $m$. In order to perform the methods, we require an estimator of the long-run variance of the error process. We propose a new difference-based estimator of the long-run error variance for the case that the error terms have an autoregressive structure. The usefulness of our methods is illustrated by an empirical application to climate data.