A criterion for estimating the largest linear homoscedastic zone in Gaussian data

Pub Date : 2024-08-06 DOI:10.1016/j.jspi.2024.106223
Jean-Marc Bardet
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Abstract

A criterion is constructed to identify the largest homoscedastic region in a Gaussian dataset. This can be reduced to a one-sided non-parametric break detection, knowing that up to a certain index the output is governed by a linear homoscedastic model, while after this index it is different (e.g. a different model, different variables, different volatility, ….). We show the convergence of the estimator of this index, with asymptotic concentration inequalities that can be exponential. A criterion and convergence results are derived when the linear homoscedastic zone is bounded by two breaks on both sides. Additionally, a criterion for choosing between zero, one, or two breaks is proposed. Monte Carlo experiments will also confirm its very good numerical performance.

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估计高斯数据中最大线性同余区的标准
我们构建了一个标准来识别高斯数据集中最大的同方差区域。这可以简化为单边非参数断裂检测,即在某一指数之前,输出由线性同方差模型控制,而在该指数之后,输出则不同(例如,不同的模型、不同的变量、不同的波动率,....)。我们展示了该指数估计值的收敛性,其渐近集中不等式可能是指数型的。当线性同余区两侧有两个断点时,我们将得出一个标准和收敛结果。此外,还提出了在零、一或两个断点之间进行选择的标准。蒙特卡罗实验也将证实其非常好的数值性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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