Robust Spectral Analysis

TL;DR

This paper introduces quantile spectral densities for analyzing cyclical behavior in time series across their entire distribution, providing a robust alternative to classical spectral methods especially under model misspecification.

Contribution

It develops a new spectral analysis method based on quantiles, enabling robust inference in nonlinear and non-Gaussian time series models.

Findings

Quantile spectral densities effectively capture cyclical behavior across distributions.

The method shows robustness and improved performance over classical spectral analysis in simulations.

Statistical properties of the estimators are established for a broad class of models.

Abstract

In this paper I introduce quantile spectral densities that summarize the cyclical behavior of time series across their whole distribution by analyzing periodicities in quantile crossings. This approach can capture systematic changes in the impact of cycles on the distribution of a time series and allows robust spectral estimation and inference in situations where the dependence structure is not accurately captured by the auto-covariance function. I study the statistical properties of quantile spectral estimators in a large class of nonlinear time series models and discuss inference both at fixed and across all frequencies. Monte Carlo experiments illustrate the advantages of quantile spectral analysis over classical methods when standard assumptions are violated.