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I know there are methods to determine the degree of polarization of multi-dimensional signals, say [Bx(t), By(t)] -> DOP(f). Is there any way to extract a DOP for given vector time series in the time domain? Thanks!

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You should probably use one of the algorithms for primary component (PCA) or independent component (ICA) investigation. They heavily relay on covatiance matrices and their eigenvalue-eigenvector decomposition.

If your time series represent an oscillation with dominant direction, the eigenvector for the maximum magnitude eigenvalue would represent that direction. If the signal is some kind of elliptic, the basis of eigenvectors would represent the oscillation ellipsoid dimensions. Degree of polarization is then easily yielded from relations of main-to-other eigenvectors magnitudes.

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