Concerning Applications of Singular Spectrum Analysis

The method of singular spectrum analysis is examined. We found that given an error estimate of the eigenvalue problem, we can determine the maximum deviations at which the frequencies of two eigenfunction can be considered as equal. This may be considered as a supplemental condition in addition to the method suggested by Vautard and Ghil (1989) to give an estimate of the divations within which the eigenvalues can be considered as equal. We have shown spurious modes may crept into an approximate solution but these spurious modes are harmless because their eigenvalues are very small. We then showed by example that if condition (2) of Vautard and Gihl is kept,the singular spectrum analysis sometimes may miss some basic frequencies.