A Test for Weak Stationarity in the Spectral Domain

Abstract

We examine tests for stability of the dynamics of a time series against alternatives that cover both local-stationarity and break points. One key feature of the tests is that the asymptotic distribution are functionals of the standard Brownian Bridge sheet in [0, 1] 2 . The tests have nontrivial power against local alternatives converging to the null hypothesis at a T −1/2 rate, where T is the sample size. We examine an easy-to-implement bootstrap analogue and present the finite-sample performance in Monte-Carlo experiment. Finally, we implement the methodology to assess the stability of the inflation dynamics in the United States and on a set of neuroscience tremor data.Date: May 8th, 2017.

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

“…, T as T → ∞, it is reasonable to formulate the null hypotheses in terms of the approximating sequences {X (u) t : t ∈ Z}. Note that the formulation of hypotheses in terms of approximating processes is rather common in this field (see, for example, Paparoditis 2009;Dette et al 2011;Hidalgo and Souza 2019;.…”