Change-Point Detection in Functional First-Order Auto-Regressive Models

Algimantas Birbilas () and Alfredas Račkauskas ()
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Algimantas Birbilas: Institute of Applied Mathematics, Vilnius University, Naugarduko g. 24, LT-03225 Vilnius, Lithuania
Alfredas Račkauskas: Institute of Applied Mathematics, Vilnius University, Naugarduko g. 24, LT-03225 Vilnius, Lithuania

Mathematics, 2024, vol. 12, issue 12, 1-25

Abstract: A sample of continuous random functions with auto-regressive structures and possible change-point of the means are considered. We present test statistics for the change-point based on a functional of partial sums. To study their asymptotic behavior, we prove functional limit theorems for polygonal line processes in the space of continuous functions. For some situations, we use a block bootstrap procedure to construct the critical region and provide applications. We also study the finite sample behavior via simulations. Eventually, we apply the statistics to a telecommunications data sample.

Keywords: mean change-point detection; functional central limit theorem; functional sample; partial sums (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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