Authors: Dette, Holger
Wu, Weichi
Title: Change point analysis in non-stationary processes - a mass excess approach
Language (ISO): en
Abstract: This paper considers the problem of testing if a sequence of means (μ t)t=1,...,n of a non-stationary time series (Xt)t=1,...,n is stable in the sense that the di fference of the means μ1 and μt between the initial time t = 1 and any other time is smaller than a given level, that is |μ1 — μt| ≤ c for all t = 1,..., n. A test for hypotheses of this type is developed using a bias corrected monotone rearranged local linear estimator and asymptotic normality of the corresponding test statistic is established. As the asymptotic variance depends on the location and order of the critical roots of the equation |μ1 — μt| = c a new bootstrap procedure is proposed to obtain critical values and its consistency is established. As a consequence we are able to quantitatively describe relevant deviations of a non-stationary sequence from its initial value. The results are illustrated by means of a simulation study and by analyzing data examples.
Subject Headings: locally stationary process
change point analysis
relevant change points
local linear estimation
Gaussian approximation
rearrangement estimators
Subject Headings (RSWK): Change-point-Problem
Issue Date: 2018
Appears in Collections:Sonderforschungsbereich (SFB) 823

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