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The computational complexity of different steps of the basic SSA isdiscussed. It is shown that the use of the general-purpose "blackbox" routines(e.g. found in packages like LAPACK) leads to huge waste of time resourcessince the special Hankel structure of the trajectory matrix is not taken intoaccount. We outline several state-of-the-art algorithms (for example,Lanczos-based truncated SVD) which can be modified to exploit the structure ofthe trajectory matrix. The key components here are hankel matrix-vectormultiplication and hankelization operator. We show that both can be computedefficiently by the means of Fast Fourier Transform. The use of these methodsyields the reduction of the worst-case computational complexity from O(N^3) toO(k N log(N)), where N is series length and k is the number of eigentriplesdesired.

Computation- and space-efficient implementation of SSA