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Department Seminar Series: Stanislav Volgushev, Quantile-based spectral analysis

Tuesday, January 20, 2015
12:00 AM
411 West Hall

This talk focuses on a novel method for the frequency domain analysis of a strictly stationary time series. We define a "new" spectrum as the Fourier transform of the differences between copulas of the pairs with different lags and the independence copula. This object is called copula spectral density kernel and allows to separate marginal and serial aspects of a time series. The copula spectral density kernel is substantially more informative than the "classical" spectral density obtained from the auto-covariances.   In particular, it provides a complete description of the copulas of pairs with arbitrary lag. We introduce a way to estimate copula spectral density kernels, describe the distributional  properties of the proposed estimator, and comment on several extensions.