Computation and SpaceEfficient Implementation of SSA
Abstract
The computational complexity of different steps of the basic SSA is discussed. It is shown that the use of the generalpurpose "blackbox" routines (e.g. found in packages like LAPACK) leads to huge waste of time resources since the special Hankel structure of the trajectory matrix is not taken into account. We outline several stateoftheart algorithms (for example, Lanczosbased truncated SVD) which can be modified to exploit the structure of the trajectory matrix. The key components here are hankel matrixvector multiplication and hankelization operator. We show that both can be computed efficiently by the means of Fast Fourier Transform. The use of these methods yields the reduction of the worstcase computational complexity from O(N^3) to O(k N log(N)), where N is series length and k is the number of eigentriples desired.
 Publication:

arXiv eprints
 Pub Date:
 November 2009
 arXiv:
 arXiv:0911.4498
 Bibcode:
 2009arXiv0911.4498K
 Keywords:

 Computer Science  Numerical Analysis
 EPrint:
 27 pages, 8 figures