White noise testing for functional time series via functional quantile autocorrelation

2026-01-14

AI Summary

This study addresses the limitations of conventional white noise tests for functional time series, which often fail to handle nonlinear dependencies, outliers, and infinite-dimensional structures while relying on moment conditions. To overcome these challenges, the authors propose a novel nonlinear white noise test based on functional quantile autocorrelations. The method characterizes temporal dependence through quantile excitation sets, constructs a global test statistic, and establishes its asymptotic distribution theory without requiring moment conditions. As the first work to incorporate functional quantile autocorrelations into white noise testing, the proposed approach exhibits strong robustness against outliers and complex nonlinear dependencies. Simulation studies and empirical analysis of high-frequency financial data demonstrate that the method significantly outperforms existing alternatives in both detection power and practical applicability.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Non-convex Optimization
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

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.

Problem

• functional time series
• white noise testing
• serial dependence
• quantile autocorrelation
• nonlinear dependence

Innovation

• functional quantile autocorrelation
• nonlinear serial dependence test
• functional time series
• robust inference
• excursion sets