EconPapers    
Economics at your fingertips  
 

Of Copulas, Quantiles, Ranks and Spectra - An L1-Approach to Spectral Analysis

Holger Dette, Marc Hallin, Tobias Kley and Stanislav Volgushev

Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: In this paper we present an alternative method for the spectral analysis of a strictly stationary time series {Yt}t2Z. We define a “new” spectrum as the Fourier transform of the differences between copulas of the pairs (Yt, Yt−k) and the independence copula. This object is called copula spectral density kernel and allows to separate marginal and serial aspects of a time series. We show that it is intrinsically related to the concept of quantile regression. Like in quantile regression, which provides more information about the conditional distribution than the classical location-scale model, the copula spectral density kernel is more informative than the spectral density obtained from the autocovariances. In particular the approach provides a complete description of the distributions of all pairs (Yt, Yt−k). Moreover, it inherits the robustness properties of classical quantile regression, because it does not require any distributional assumptions such as the existence of finite moments. In order to estimate the copula spectral density kernel we introduce rank-based Laplace periodograms which are calculated as bilinear forms of weighted L1-projections of the ranks of the observed time series onto a harmonic regression model. We establish the asymptotic distribution of those periodograms, and the consistency of adequately smoothed versions. The finite-sample properties of the new methodology, and its potential for applications are briefly investigated by simulations and a short empirical example.

Keywords: Time series; spectral analysis; periodogram; quantile regression; copulas; ranks; time reversibility (search for similar items in EconPapers)
Pages: 45 p.
Date: 2011-12
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Published by:

Downloads: (external link)
https://dipot.ulb.ac.be/dspace/bitstream/2013/1047 ... GUSHEV-ofcopulas.pdf 2011-038-DETTE_HALLIN_KLEY_VOLGUSHEV-ofcopulas (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eca:wpaper:2013/104763

Ordering information: This working paper can be ordered from
http://hdl.handle.ne ... lb.ac.be:2013/104763

Access Statistics for this paper

More papers in Working Papers ECARES from ULB -- Universite Libre de Bruxelles Contact information at EDIRC.
Bibliographic data for series maintained by Benoit Pauwels ().

 
Page updated 2025-03-30
Handle: RePEc:eca:wpaper:2013/104763