  In this paper, we present an alternative method for the spectral analysis of
a univariate, strictly stationary time series $\{Y_t\}_{t\in \mathbb {Z}}$. We
define a "new" spectrum as the Fourier transform of the differences between
copulas of the pairs $(Y_t,Y_{t-k})$ and the independence copula. This object
is called a copula spectral density kernel and allows to separate the marginal
and serial aspects of a time series. We show that this spectrum is closely
related to the concept of quantile regression. Like quantile regression, which
provides much more information about conditional distributions than classical
location-scale regression models, copula spectral density kernels are more
informative than traditional spectral densities obtained from classical
autocovariances. In particular, copula spectral density kernels, in their
population 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 do
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 $L_1$-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.
