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Title: Robust conditional spectral analysis of replicated time series Authors:  Zeda Li - City University of New York (United States) [presenting]
Abstract: Traditional spectral analysis, which is based on the Fourier transform of the autocovariance, focuses on summarizing the cyclical behavior of a single time series. However, this type of analysis is subject to two major limitations: first, being covariance-based, it cannot accommodate heavy-tail dependence and infinite variance, and detect dynamics in time-irreversibility and kurtosis; second, focusing on a single time series, it is unable to analyze multiple time series and to quantify how their spectra are associated with other variables. We propose a new nonparametric approach to the spectral analysis of multiple time series and the associated covariates. The procedure is based on the copula spectral density kernel, which inherits the robustness properties of classical quantile regression and does not require any distributional assumptions, such as the existence of finite moments. Copula spectral density kernel of different pairs are modeled jointly as a matrix to allow flexible smoothing. Through a tensor-product spline model of Cholesky components of outcome-dependent copula spectral densities, the approach provides flexible nonparametric estimates of copula spectral density matrix as nonparametric functions of frequency and outcome while preserving geometric constraints.