English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we present an alternative method for the spectral analysis ofa univariate, strictly stationary time series $\{Y_t\}_{t\in \mathbb {Z}}$. Wedefine a "new" spectrum as the Fourier transform of the differences betweencopulas of the pairs $(Y_t,Y_{t-k})$ and the independence copula. This objectis called a copula spectral density kernel and allows to separate the marginaland serial aspects of a time series. We show that this spectrum is closelyrelated to the concept of quantile regression. Like quantile regression, whichprovides much more information about conditional distributions than classicallocation-scale regression models, copula spectral density kernels are moreinformative than traditional spectral densities obtained from classicalautocovariances. In particular, copula spectral density kernels, in theirpopulation versions, provide (asymptotically provide, in their sample versions)a complete description of the copulas of all pairs $(Y_t,Y_{t-k})$. Moreover,they inherit the robustness properties of classical quantile regression, and donot require any distributional assumptions such as the existence of finitemoments. In order to estimate the copula spectral density kernel, we introducerank-based Laplace periodograms which are calculated as bilinear forms ofweighted $L_1$-projections of the ranks of the observed time series onto aharmonic regression model. We establish the asymptotic distribution of thoseperiodograms, and the consistency of adequately smoothed versions. Thefinite-sample properties of the new methodology, and its potential forapplications are briefly investigated by simulations and a short empiricalexample.

Of copulas, quantiles, ranks and spectra: An $L_1$-approach to spectral analysis