A key step in separating signal from noise using Singular Spectrum Analysis (SSA) is grouping, which is often done subjectively. In this article a method which enables the identification of statistically significant groups for the grouping step in SSA is presented. The proposed procedure provides a more objective and reliable approach for separating noise from the main signal in SSA. We utilize the w- correlation and test if it close or equal to zero. A wild bootstrap approach is used to determine the distribution of the w-correlation. To identify an ideal number of groupings which leads to almost perfect separation of the noise and signal, a given number of groups are tested, necessitating accounting for multiplicity. The effectiveness of our method in identifying the best group is demonstrated through a simulation study, furthermore, we have applied the approach to real world data in the context of neuroimaging. This research provides a valuable contribution to the field of SSA and offers important insights into the statistical properties of the w-correlation distribution. The results obtained from the simulation studies and analysis of real-world data demonstrate the effectiveness of the proposed approach in identifying the best groupings for SSA.

翻译：使用奇异谱分析（SSA）分离信号与噪声的关键步骤是分组，而这一过程通常依赖主观判断。本文提出了一种方法，能够在SSA的分组步骤中识别具有统计显著性的组别。该程序为SSA中从主信号中分离噪声提供了更客观、可靠的手段。我们利用w-相关性，检验其是否接近或等于零，并采用野刀切法确定w-相关性的分布。为识别能够实现噪声与信号近乎完美分离的理想分组数量，我们对给定数量的组别进行检验，这需要处理多重比较问题。通过模拟研究验证了该方法在识别最佳组别方面的有效性，此外，我们还将该方法应用于神经影像领域的真实数据。本研究为SSA领域做出了重要贡献，并为w-相关性分布的统计特性提供了重要见解。模拟研究与真实数据分析结果均表明，所提方法在识别SSA最佳组别方面具有显著有效性。