Detecting deviations from second-order stationarity in locally stationary functional time series

A. Bücher, H. Dette, F. Heinrichs

A time-domain test for the assumption of second order stationarity of a functional time series is proposed. The test is based on combining individual cumulative sum tests which are designed to be sensitive to changes in the mean, variance and autocovariance operators, respectively. The combination of their dependent p-values relies on a joint dependent block multiplier bootstrap of the individual test statistics. Conditions under which the proposed combined testing procedure is asymptotically valid under stationarity are provided.

Palabras clave: alpha-mixing CUSUM-test auto-covariance operator block multiplier bootstrap change points

A. Torres Signes, M. P. Frías Bustamante, M. D. Ruiz-Medina

D. C. Gamboa Pinilla, A. M. Alonso, D. Peña

J. D. Bermúdez Edo, A. Rubio Fornés, E. Vercher González