## Statistics Seminar Series

Thursday, October 9, 4:10pm, MSB 1147 (Colloquium Room)
Refreshments at 3:30pm in MSB 4110 (Statistics Lounge)

Speaker: Holger Dette (Ruhr-Universität Bochum, Germany)

Title: “Quantile based spectral analysis”

Abstract: We present an alternative method for the spectral analysis of strictly stationary time series $\{Y_t\}_{t\in \Z}$ by defining a new'' spectrum as the Fourier transform of the differences between copulas of the pairs $(Y_t,Y_{t-k})$ and the independence copula. This object is called a {\it copula spectral density kernel} and allows to separate the marginal and serial aspects of a time series. We show that this spectrum is closely related to the concept of quantile regression. Like quantile regression, which provides much more information about conditional distributions than classical location-scale regression models, copula spectral density kernels are more informative than traditional spectral densities obtained from classical autocovariances. Moreover, they inherit the robustness properties of classical quantile regression, and do not require any distributional assumptions such as the existence of finite moments. We establish the asymptotic distribution theory of corresponding estimates and investigate the finite-sample properties of the new methodology.