Matlabs commands for analyzing vector time series (e.g., vgxvarx, vgxproc) accept exogenous inputs. I understand the explanation that each of p inputs can have q paths with r observations, requiring (p)x(q)x(r) data. However, the vgx analysis commands accept one such block of data per time series, i.e., (p)x(q)x(r)x(n) data, where n is the number of time series.

Does anyone know the motivation for segregating the exogenous inputs into 1 set per time series? It seems to me that if you have a common set of exogenous inputs, you should be able to define the dependence of any time series on any input.

For context, I found that the modelling of exogenous inputs seem to be diverse.

In one example, the number of exogenous inputs is arbitrary, and the coupling between time series and inputs is many-to-many: http://faculty.washington.edu/ezivot/econ584/notes/varModels.pdf.

In another, the number of exogenous inputs is also arbitrary, and lags are incorporated into the model: http://cran.r-project.org/web/packages/MTS/MTS.pdf.

Wikipedia shows that for the nonvector model, lags of the exogenous inputs are mathematically represented: http://en.wikipedia.org/wiki/Autoregressive–moving-average_model. I'm aware from a previous post that you can represent lags of an input as additional inputs, so the absence of exogenous lags in the mathematical expression is not a show stopper.

This question seems to both Matlab-specific and concept-oriented, so in addition to comp.soft-sys-matlab, I've posted it to both Cross Validated and Stack Overflow:

  • $\begingroup$ Cross-posting is not a good practice. $\endgroup$ – Aksakal May 28 '15 at 20:51
  • $\begingroup$ I appreciate your answer to the question. However, about cross posting: I realize that this is a tenet from usenet days, and I had this discussion on a LaTeX forum. My impression is that there is no consensus. The pros is that it can reach multiple audiences, which makes sense if they are all relevant. The con is fragmentation, which can be ameliorated by posting links to the other forums. Bandwidth is no longer an issue as it was in usenet days. The discussion can be more than can fit in a comment, and I don't mind having it via another means (our firewall won't access chat forums, though). $\endgroup$ – StatSmartWannaB May 28 '15 at 21:52
  • $\begingroup$ BTW, regarding the discussion on the LaTeX forum, the moderator approved crossposting so long as links were supplied. I've tried to adhere to that. $\endgroup$ – StatSmartWannaB May 28 '15 at 21:53

It seems to me that if you have a common set of exogenous inputs, you should be able to define the dependence of any time series on any input.

That will only work if you have a lot of data. In econometrics that's not the case. For instance, if you have 10 variables, one lag and 15 exogenous inputs, you're talking about 10x(10+15)=250 coefficients and 10(10-1)/2=45 correlations, i.e. 295 parameters. That's a lot to estimate reliably. It's even more difficult to interpret.

That's why you try to sparse the matrices as much as possible. Not using every exogenous variable for every dependent variable equation is one way to proceed.

  • $\begingroup$ That makes a lot of sense. By associating sets of inputs with individual time series, you're effectively allowing only block matrices of dependencies. Thanks. $\endgroup$ – StatSmartWannaB May 28 '15 at 21:34
  • $\begingroup$ I wish there was a better way in matlab to capture the model structure than the block matrices. They are hard to read and set up. $\endgroup$ – Aksakal May 28 '15 at 22:03
  • $\begingroup$ I don't think the method used by vgx function for the exogenous inputs is bad. I just didn't understand what they were doing. I much prefer the vgx method than for me to set it up myself. :) $\endgroup$ – StatSmartWannaB May 29 '15 at 3:50

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