ABSTRACT It is well known that a neighbourhood problem exists between stationarity and random walk with correlated error for any finite sample size n. That is, any stationary process is approximated by random walk with correlated error for any finite n. Hence, one cannot distinguish between them easily. In this article, we propose a stationarity test based on nonparametric density that resolves the neighbourhood problem successfully. Our stationarity test also emerges as a successful long-range dependence (LRD) stationarity test. Note that there is a similar neighbourhood problem between LRD stationarity and LRD non-stationarity [Samorodnitsky, G. (2006), ‘Long Range Dependence’, Foundations and Trends in Stochastic Systems, 1, 163–257].

中文翻译：

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基于密度法的平稳性检验

摘要众所周知，对于任何有限样本大小n，在平稳性和具有相关误差的随机游走之间存在邻域问题。也就是说，对于任何有限 n，任何平稳过程都可以通过具有相关误差的随机游走来近似。因此，人们无法轻易区分它们。在本文中，我们提出了一种基于非参数密度的平稳性检验，它成功地解决了邻域问题。我们的平稳性检验也作为成功的长期依赖 (LRD) 平稳性检验而出现。请注意，LRD 平稳性和 LRD 非平稳性之间存在类似的邻域问题 [Samorodnitsky, G. (2006), 'Long Range Dependence', Foundations and Trends in Stochastic Systems, 1, 163–257]。