THE INTEGRATED COPULA SPECTRUM

Yu‐ichi Goto

doi:10.1214/22-AOS2240

THE INTEGRATED COPULA SPECTRUM

2022-12-01

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DOI：10.1214/22-AOS2240

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Frequency domain methods form a ubiquitous part of the statistical tool-box for time-series analysis. In recent years, considerable interest has been given to the development of new spectral methodology and tools capturing dynamics in the entire joint distributions, and thus avoiding the limitations of classical, L2-based spectral methods. Most of the spectral concepts proposed in that literature suffer from one major drawback, though: their estimation re-quires the choice of a smoothing parameter, which has a considerable impact on estimation quality and poses challenges for statistical inference. In this pa-per, associated with the concept of a copula-based spectrum, we introduce the notion of a copula spectral distribution function or integrated copula spec-trum. This integrated copula spectrum retains the advantages of copula-based spectra but can be estimated without the need for smoothing parameters. We provide such estimators, along with a thorough theoretical analysis, based on a functional central limit theorem, of their asymptotic properties. We leverage these results to test various hypotheses that cannot be addressed by classical spectral methods, such as the lack of time reversibility or asymmetry in tail dynamics.

Keywords:

Copula

ranks

time series

frequency domain

time reversibility

THE INTEGRATED COPULA SPECTRUM

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