A Bootstrap-Based KPSS Test for Functional Time Series

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 against many alternative hypotheses. We derive the asymptotic distribution of the simple bootstrap-based KPSS test statistic for functional time series, which proves the bootstrap validity on average. Simulation studies are then conducted to examine the performance of the proposed KPSS tests in small and moderate sample sizes. The results demonstrate that the bootstrap-based functional KPSS test has good empirical size and power. Moreover, its implementation is more efficient than the existing KPSS test for functional time series.