Singular Spectrum Analysis with R by Nina Golyandina Anton Korobeynikov & Anatoly Zhigljavsky

Author:Nina Golyandina, Anton Korobeynikov & Anatoly Zhigljavsky
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

3.1.2 Algorithms

Although the LRR approximating the time series is usually used for forecasting, it can also be helpful for construction of the signal model. Hence we introduce an algorithm for calculation of the min-norm LRR coefficients.

Algorithm 3.1 Estimation of the signal LRR

The next algorithm shows how the parameters μ i in can be estimated from the roots of the characteristic polynomial of an LRR governing this time series (see Sect. 2.​1.​2.​2 for a description of the relation between LRRs and their characteristic polynomials). The given LRR is an estimate of an LRR governing a series of rank r; therefore, only r roots correspond to the signal, while the other roots are extraneous. Since frequently (but not always!) the signal roots for the min-norm LRR have larger moduli than the extraneous roots, we can select signal roots with large absolute values among the whole set of roots.

Algorithm 3.2 Estimation of the signal roots through characteristic polynomial of LRR

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