note-for-ssa.md

SSA使用指南

参考文献：

📖 [1] Hassani, H. (2007). "Singular spectrum analysis: methodology and comparison."

📖 [2] Vautard, R., P. Yiou and M. Ghil (1992). "Singular-Spectrum Analysis - a Toolkit for Short, Noisy Chaotic Signals." Physica D 58(1-4): 95-126.

Aim^[1]^

decomposite the original time series ➡️ independent & interpretable components

• Finding trend of different resolution
• Smoothing
• Extraction of seasonality components
• Change-point detection
• ......

decomposite

L: window length ( embedding dimension) T: period N: length of time series

条件：

1. L < $\frac{N}{2}$
2. L = kT (k is constant)
3. successful at $T \in(\frac{L}{5},L)$ ^[2]^

reconstruct

information:

1. every harmonic component produce 2 eigentriples with close singular values.
2. a pure noise series produce slowly decreasing eigenvalue spectra.
3. pairewise scatterplot