Singular Spectrum Analysis by Hossein Hassani & Rahim Mahmoudvand

Author:Hossein Hassani & Rahim Mahmoudvand
Language: eng
Format: epub
Publisher: Palgrave Macmillan UK, London

where indicates that the output of the first step is a block Hankel trajectory matrix in a vertical form.

Step 2: SVD. In this step, the SVD of is performed. Denote by the eigenvalues of , arranged in decreasing order and by , the corresponding eigenvectors, and . Note that the structure of the matrix is as follows:

(2.5)

The structure of the matrix is similar to the variance-covariance matrix in classical multivariate statistical analysis literature. The matrix , which is used in univariate SSA, for the series , appears along the diagonal, and the products of two Hankel matrices , which are related to the series and , appear in the off-diagonal.

The SVD of can be written as where

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