Peter Urbani' Statistics - An Introduction to Singular Spectrum Analysis
An Introduction to Singular Spectrum Analysis (SSA)
Most of you will be familiar with Principal Component Analysis (PCA), used mostly in fixed income models where the first three ordered principal components, or dominant eigenvalues, are deemed to represent the level, slope and curvature of the yield curve. This month we review a related method namely Singular Spectrum Analysis (SSA). I have also included a worked example and a spreadsheet implementation that can be downloaded here.
The mathematics behind SSA has multiple names. It is also known as: Proper Orthogonal Decomposition, PCA, Principal Value Decomposition, Singular Value Decomposition, Singular System Analysis, bi-orthogonal decomposition, Karmen Loeve decomposition and the Caterpillar method.
While most traditional econometric time series analysis substantially lies in the time domain, spectral analysis is performed in the frequency domain. The idea dates back to the 1960s and even earlier to a paper by Edward Lorenz, who proposed its use for the measurement and forecasting of localised weather phenomenon. Its use has mostly been in the fields of Geostatistics and Digital Signal Processing until fairly recently with the recent interest in the Mane ......................
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