njit-etd2003-081 - New Jersey Institute of Technology

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3.12 Partial Coherence Analysis
3.12.1 Multivariate Analysis
The above methods can be extended to examine the correlation structure between
several simultaneously recorded signals. This is called a multivariate analysis, and is
equivalent to multivariate regression analysis, except that parameters are estimated at
each frequency of interest.
Two related questions which can be addressed by such analysis are 1) whether
the correlation between two signals results from the common (linear) influence of a third
signal, and 2) whether a third signal is capable of predicting the correlation between two
signals. Both these questions can be addressed by estimating the partial coherence, and
partial phase which characterize the correlation between the two original signals after
removing the common linear effects of the third (predictor) signal from each. This
multivariate analysis can be performed on any combination of point process and/or time
series data [64].
3.12.2 Partial Spectra
The starting point for the multivariate analysis is the estimates of second order spectra
described in Section 3.10 of the coherence analysis, with the requirement of three
simultaneously recorded signals and spectral estimates which have been estimated with
the same segment length, T. For example, to estimate the partial correlation between
point process N 0 and time series x, with time series y as predictor, one starts by defining
partial spectra, estimates of which are then used to construct estimates of the other