V.V. Isakevich, L.V. Grunskaya, D.V. Isakevich, L.T. Sushkova
Both spectral analysis method and methods based on signal represenations in the bases of covariance matrix ei-genvectors. It can be shown that eigenvectors of the covariance matrix are asymptotically invariant to additive non-correlated stationary noise of the investigated time series. Eigenvectors are completely determined by the co-variance matrix of time series and the time interval of analysis chosen by an investigator. The basis of eigenvectors is orthonormal. The eigenvectors basis is defined not by the choice of the researcher but by the time series itself so one may hope that this basis will express the properties of the invastigated natural object. Each of these vectors should correspond to the definite time series component.
One may also hope that it will be useful while searching the complicated periodic components in the time series (i.e. detection of the modulations). The method of spectral analysis should be modified in order to research not the time series itself but the covariance matrix eigenvectors for this time series.
Every eigenvector has its own energetic part to the time series which is defined as the corresponding eigenvalue-to-trace ratio. So the structure analysis of eigenvectors which bring the information about the specific properties of the natural phenomena allows to detect these properties depending the energetic part of the eigenvector in the time series. Examples of the results of eigenvector semantic analysis are given for electric field observations on scope of stations.