We distinguish the following data structures
I Time series data:
I fxt ; t = 1; : : : ; Tg, univariate series, e.g. a price series:
Its path over time is modeled. The path may also depend on third variables.
I Multivariate, e.g. several price series:
Their individual as well as their common dynamics is modeled. Third variables
may be included.
I Cross sectional data are observed at a single point of time for several
individuals, countries, assets, etc.,
xi , i = 1; : : : ;N.
The interest lies in modeling the distinction of single individuals, the
heterogeneity across individuals.
hi Nabeel. All those models you mention do have shocks but they are actually seeking to model the variables to be explained by them. This means that their objective is not quite to "measure" shocks. BUT if they are really able to closely model the variables to be explained, then they can be used as an indirect way to obtain measures of the shocks. Therefore, since no variable is born alone but it is interacting with others, the best way to do what I think you are trying to do is inside big multivariate models (ie, including many variables to be explained). Then there appears the phantom of all these models: too many parameters to do that. BUT if you can solve this problem, you may end up with good measures of structural shocks (like those coming from an Structural VAR - SVAR).
Of course, but those "appropriate restrictions" have zero value in the case of over-parametrized too-small-to-be-useful VAR models.
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