A portmanteau test for multivariate non-stationary functional time series with an increasing number of lags

TL;DR

This paper introduces a new portmanteau test for multivariate locally stationary functional time series to assess white noise assumptions, using bootstrap methods and Gaussian approximation, without dimension reduction.

Contribution

It develops a specialized portmanteau test for functional time series that handles non-standard distributions and increasing lags, with a novel Gaussian approximation for degenerate U-statistics.

Findings

The test effectively detects departures from white noise.

Bootstrap procedure accurately implements the test.

Method adapts well to complex data structures.

Abstract

Multivariate locally stationary functional time series provide a flexible framework for modeling complex data structures exhibiting both temporal and spatial dependencies while allowing for time-varying data generating mechanism. In this paper, we introduce a specialized portmanteau-type test tailored for assessing white noise assumptions for multivariate locally stationary functional time series without dimension reduction. A simple bootstrap procedure is proposed to implement the test because the limiting distribution can be non-standard or even does not exist. Our approach is based on a new Gaussian approximation result for a maximum of degenerate $U$-statistics of second-order functional time series, which is of independent interest. Through theoretical analysis and simulation studies, we demonstrate the efficacy and adaptability of the proposed method in detecting departures from white noise assumptions in multivariate locally stationary functional time series.