<p>In this paper, we propose a computationally efficient and theoretically justified group least absolute shrinkage and selection operator (Group LASSO; GLASSO) method for estimating multiple change-points in a piecewise stationary generalized integer-valued autoregressive process. The proposed method is particularly suitable for finite samples with many closely spaced change-points. We further develop an efficient implementation that combines least angle regression and optimal partitioning (OP). The overall computational complexity is <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$O(Kn+K^2)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <mi>K</mi> <mi>n</mi> <mo>+</mo> <msup> <mi>K</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> when OP is used and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$O(Kn+K^3)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <mi>K</mi> <mi>n</mi> <mo>+</mo> <msup> <mi>K</mi> <mn>3</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> when the backward elimination algorithm is used. In addition, we propose an iterative procedure for selecting a data-driven order <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\tilde{p}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>p</mi> <mo stretchy="false">~</mo> </mover> </math></EquationSource> </InlineEquation>, which achieves satisfactory performance with relatively low computational cost. Simulation studies and a real data analysis demonstrate that the proposed method and iterative procedure perform well in practice and support the theoretical results.</p>

Group LASSO for multiple change-point detection in a generalized integer-valued autoregressive model

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2026年7月24日

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Danshu Sheng,
Jiao Hua,
Jinxian Xu,
Dehui Wang,
Shuilin Jin

摘要

In this paper, we propose a computationally efficient and theoretically justified group least absolute shrinkage and selection operator (Group LASSO; GLASSO) method for estimating multiple change-points in a piecewise stationary generalized integer-valued autoregressive process. The proposed method is particularly suitable for finite samples with many closely spaced change-points. We further develop an efficient implementation that combines least angle regression and optimal partitioning (OP). The overall computational complexity is $O(Kn+K^2)$ $O (K n + K^{2})$ when OP is used and $O(Kn+K^3)$ $O (K n + K^{3})$ when the backward elimination algorithm is used. In addition, we propose an iterative procedure for selecting a data-driven order $\tilde{p}$ $\tilde{p}$ , which achieves satisfactory performance with relatively low computational cost. Simulation studies and a real data analysis demonstrate that the proposed method and iterative procedure perform well in practice and support the theoretical results.