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Journal of Time Series Analysis
Article . 2025 . Peer-reviewed
License: CC BY
Data sources: Crossref
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https://dx.doi.org/10.48550/ar...
Article . 2025
License: CC BY NC ND
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Estimation of Change Points for Non‐Linear (Auto‐)Regressive Processes Using Neural Network Functions

Authors: Claudia Kirch; Stefanie Schwaar;

Estimation of Change Points for Non‐Linear (Auto‐)Regressive Processes Using Neural Network Functions

Abstract

ABSTRACTIn this paper, we propose a new test for the detection of a change in a non‐linear (auto‐)regressive time series as well as a corresponding estimator for the unknown time point of the change. To this end, we consider an at‐most‐one‐change model and approximate the unknown (auto‐)regression function by a neural network with one hidden layer. It is shown that the test has asymptotic power of one for a wide range of alternatives, not restricted to changes in the mean of the time series. Furthermore, we prove that the corresponding estimator converges to the true change point with the optimal rate and derive the asymptotic distribution. Some simulations illustrate the behavior of the estimator with a special focus on the misspecified case, where the true regression function is not given by a neural network. Finally, we apply the estimator to some financial data.

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Keywords

non-linear autoregressive processes, change point estimator, semi-parametric statistic, FOS: Mathematics, Mathematics - Statistics Theory, misspecification, Statistics Theory (math.ST)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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