On Singular Spectrum Analysis And Stepwise Time Series Reconstruction
On Singular Spectrum Analysis And Stepwise Time Series Reconstruction
复制标题
DOI：
10.1111/jtsa.12479
复制
发表时间：
2019-07
影响因子：
0.9
通讯作者：
D. Poskitt
中科院分区：
文献类型：
--
作者：
D. Poskitt
本文提供了奇异谱分析 (SSA) 新方法的详细统计分析。它检查了使用重新缩放的轨迹（RT-SSA）构建的 SSA，并在有关观测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 RT-SSA 大样本特性中隐含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。通过涉及趋势平稳和差异平稳过程以及带漂移的随机游走的数值示例说明了理论结果的操作。对 S&P 500 指数的分析也可以作为展示逐步 RT-SSA 处理方法的实际影响的工具。
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.