White noise testing for functional time series via functional quantile autocorrelation

TL;DR

This paper introduces a new nonlinear testing framework based on functional quantile autocorrelation to detect serial dependence in functional time series, offering robustness and improved power over existing methods.

Contribution

It develops a novel, robust testing approach using quantile autocorrelation for functional time series, with proven asymptotic properties and superior performance in simulations.

Findings

The proposed tests effectively detect complex serial dependence.

The tests are robust to outliers and nonlinear dependencies.

Simulation studies show superior power compared to existing methods.

Abstract

We introduce a novel class of nonlinear tests for serial dependence in functional time series, grounded in the functional quantile autocorrelation framework. Unlike traditional approaches based on the classical autocovariance kernel, the functional quantile autocorrelation framework leverages quantile-based excursion sets to robustly capture temporal dependence within infinite-dimensional functional data, accommodating potential outliers and complex nonlinear dependencies. We propose omnibus test statistics and study their asymptotic properties under both known and estimated quantile curves, establishing their asymptotic distribution and consistency under mild assumptions. In particular, no moment conditions are required for the validity of the tests. Extensive simulations and an application to high-frequency financial functional time series demonstrate the methodology's effectiveness, reliably detecting complex serial dependence with superior power relative to several existing tests. This work expands the toolkit for functional time series, providing a robust framework for inference in settings where traditional methods may fail.