07.05.2018 15:00 Dr. Tobias Kley, Berlin:
Quantile-Based Spectral Analysis of Time SeriesB 349 (Theresienstr. 39, 80333 München)

Classical methods for the spectral analysis of time series account for covariance-related serial dependencies. This talk will begin with a brief introduction to these traditional procedures. Then, an alternative method is presented, where, instead of covariances, differences of copulas of pairs of observations and the independence copula are used to quantify serial dependencies. The Fourier transformation of these copulas is considered and used to define quantile-based spectral quantities. They allow to separate marginal and serial aspects of a time series and intrinsically provide more information about the conditional distribution than the classical location-scale model. Thus, quantile-based spectral analysis is more informative than the traditional spectral analysis based on covariances. For an observed time series the new spectral quantities are then estimated. The asymptotic properties, including the order of the bias and process convergence, of the estimator (a function of two quantile levels) are established. The results are applicable without restrictive distributional assumptions such as the existence of finite moments and only a weak form of mixing, such as alpha-mixing, is required.