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Dette, Holger; Hallin, Marc; Kley, Tobias; Volgushev, Stanislav

Of copulas, quantiles, ranks and spectra: an \(L_{1}\)-approach to spectral analysis. (English) Zbl 1337.62286

Bernoulli 21, No. 2, 781-831 (2015).
The authors introduce an alternative method for spectral analysis of univariate stationary time series. The spectral analysis is based on two spectral kernel densities: Laplace and copula. According to these spectral kernel densities, estimation is based on Laplace and copula periodograms. Asymptotic properties of Laplace and copula periodogram kernels are introduced and discussed in Section 3. Smoothed versions of the introduced periodograms are considered in Section 4. In the last section, the authors provide some simulation studies to illustrate properties of the earlier obtained estimators.
Reviewer: Miroslav M. Ristić (Niš)

Cited in 3 Reviews
Cited in 24 Documents

MSC:

62M15 Inference from stochastic processes and spectral analysis
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

Keywords:

copulas; periodogram; quantile regression; ranks; spectral analysis; time reversibility; time series

Software:

quantilogram
PDFBibTeX XMLCite
\textit{H. Dette} et al., Bernoulli 21, No. 2, 781--831 (2015; Zbl 1337.62286)
Full Text: DOI arXiv Euclid

References:

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