This article provides a detailed statistical analysis of a new approach to singular spectrum analysis (SSA). It examines SSA constructed using re‐scaled trajectories (RT‐SSA) and presents a theoretical analysis of RT‐SSA under very general conditions concerning the structure of the observed series. The spectral features of population ensemble models implicit in the large sample properties of RT‐SSA are investigated, motivating a new time series modelling methodology based on a stepwise application of RT‐SSA. The operation of the theoretical results is illustrated via numerical examples involving trend stationary and difference stationary processes, and a random walk with drift. An analysis of the S&P 500 index also serves as a vehicle to demonstrate the practical impact of the stepwise RT‐SSA processing methodology.

中文翻译：

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关于奇异谱分析和逐步时间序列重建

本文对奇异谱分析 (SSA) 的新方法进行了详细的统计分析。它检查了使用重新缩放的轨迹 (RT-SSA) 构建的 SSA，并在关于观察序列结构的非常一般的条件下对 RT-SSA 进行了理论分析。研究了隐含在 RT-SSA 的大样本特性中的群体集成模型的光谱特征，激发了一种基于 RT-SSA 逐步应用的新时间序列建模方法。理论结果的操作通过涉及趋势平稳和差分平稳过程以及带有漂移的随机游走的数值例子来说明。对标准普尔 500 指数的分析也可作为证明逐步 RT-SSA 处理方法的实际影响的工具。