A Portmanteau-type test for detecting serial correlation in locally stationary functional time series

TL;DR

This paper extends the Portmanteau test to locally stationary functional time series, providing a bootstrap-based method to detect serial correlation with proven asymptotic properties.

Contribution

It introduces a novel Portmanteau-type test for functional time series and establishes its asymptotic validity using a block multiplier bootstrap.

Findings

Test maintains correct level asymptotically

Test is consistent against general alternatives

Bootstrap procedure effectively approximates critical values

Abstract

The Portmanteau test provides the vanilla method for detecting serial correlations in classical univariate time series analysis. The method is extended to the case of observations from a locally stationary functional time series. Asymptotic critical values are obtained by a suitable block multiplier bootstrap procedure. The test is shown to asymptotically hold its level and to be consistent against general alternatives.