In this paper, we propose a unit root test for functional time series. We derive a new analytical framework for nonstationary functional time series. Specifically, for the proposed test statistic, we derive its limit distribution under the null hypothesis of a random walk and its asymptotic...

In this study, we examine bootstrap methods to construct a generalized KPSS test for functional time series. Bootstrap-based functional testing provides an intuitive and efficient estimation of the distribution of the generalized KPSS test statistic and is capable of achieving non-trivial powers...