Quantile Spectral Processes: Asymptotic Analysis and Inference

By Tobias Kley, Stanislav Volgushev, Holger Dette, Marc Hallin. 2014

70 citations recorded by the source corpus.

Quantile-and copula-related spectral concepts recently have been considered by various authors. Those spectra, in their most general form, provide a full characterization of the copulas associated with the pairs (Xt,Xt-k) in a process (Xt )t Z, and account for important dynamic features, such as changes in the conditional shape (skewness, kurtosis), time-irreversibility, or dependence in the extremes that their traditional counterparts cannot capture. Despite various proposals for estimation strategies, only quite incomplete asymptotic distributional results are available so far for the proposed estimators, which constitutes an important obstacle for their practical application. In this paper, we provide a detailed asymptotic analysis of a class of smoothed rank-based cross-periodograms associated with the copula spectral density kernels introduced in Dette et al. [Bernoulli 21 (2015) 781-831].We show that, for a very general class of (possibly nonlinear) processes, properly scaled and centered smoothed versions of those cross-periodograms, indexed by couples of quantile levels, converge weakly, as stochastic processes, to Gaussian processes. A first application of those results is the construction of asymptotic confidence intervals for copula spectral density kernels. The same convergence results also provide asymptotic distributions (under serially dependent observations) for a new class of rank-based spectral methods involving the Fourier transforms of rank-based serial statistics such as the Spearman, Blomqvist or Gini autocovariance coefficients.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/db052919d28bceaf98f8b37b38f1d56c23f0000b

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Citations in the corpus

The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series (2014, methodology): “Fourier domain approach for test statistics based on distributions. Further development in the Fourier domain approach has been made by Hagemann (2013) and Dette et al. (2015). See also Li (2014) and Kley et al. (2016). The quantilogram has recently been applied to stock returns and exchange rates, ”
Quantile spectral analysis for locally stationary time series (2014, background): “That thread of literature also includes Li (2012, 2014a,b), Kley et al. (2016) and Lee and Subba Rao (2012).”
Quantile coherency: A general measure for dependence between cyclical economic variables (2015, unknown): “This comment also applies to Kley et al. (2016).”