Centered and non-centered principal component analyses in the frequency domain. (English) Zbl 1178.62066
Summary: Given a stationary multidimensional process and the process which is deduced after centering, we wish to study possible links between the principal component analyses, in the frequency domain, of these two processes. It is well known that there is, a priori, no obvious relationship between the centered and non-centered principal component analyses in the temporal domain. Furthermore, we also know that principal component analysis in the frequency domain is reduced to principal component analysis of each spectral component. We show the remarkable result that the centered and non-centered principal component analyses in the frequency domain are equal except for a given frequency.
MSC:
| 62H25 | Factor analysis and principal components; correspondence analysis |
| 62M15 | Inference from stochastic processes and spectral analysis |
Software:
astsaReferences:
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