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

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.
Comment: Keywords: Autocovariance operator, Block multiplier bootstrap, Functional white noise, Time domain test