SVD is not applicable to time series analysis? I am studying a deconvolution problem for which observations include noise. I am considering using one of several common regularization methods, including Tikhonov's solution, truncated Singular Value Decomposition (SVD), or Wiener filter.

A manuscript I am reading, Riel and Berkhout, "Resolution in seismic trace inversion by parameter estimation" in Geophysics, 50(9), pp. 1440-1455, 1985, compares analysis in the Fourier domain with general SVD analysis:


  Examples where SVD-based techniques may be used while Fourier
  techniques are no longer applicable are: time-invariant filtering,
  space-variant wave field extrapolation [...], and linear parameter
  estimation problems. Furthermore, in many nonlinear problems
  linearization is meaningful, again allowing application of the SVD.
  The nonlinear problem treated is such an example. In our opinion many
  problem areas in seismic exploration stand to benefit from an analysis
  involving the SVD. However, there are some limitations compared to
  Fourier analysis. For instance, SVD is not applicable to time-series
  analysis. Furthermore, the eigenvectors and eigenvalues do not, in
  general, have the clear physical meaning the sinusoids and their
  amplitudes in Fourier analysis do. For these reasons SVD-based
  methods should, when possible, not replace Fourier analysis methods,
  but rather be used in conjunction with them.


I was surprised to read that "SVD is not applicable to time-series analysis." It is not clear to me that this is the case, and indeed the authors use SVD to construct an inverse filter for their convoluted time series.

I wonder if there is common knowledge in the DSP community regarding SVD's unsuitability for time series analysis in general or specific aspects, as this is the first time I have come across this statement. (It is also surprising to find no SVD or eigenanalysis tag.) Thanks in advance.
SVD of multi-variate time-series is of course very common.  The point I think the author is making is that SVD cannot meaningfully be directly applied to a univariate time-series, instead it is commonly used indirectly to explore the main eigenvalues of a transition matrix, estimated from observed trajectories of a certain length. see http://en.wikipedia.org/wiki/Singular_spectrum_analysis .  SSA assumes the time-series is stationary and can be modeled as Markov.