I'm using Wooldridge's textbook as my guide for a time-series cross-sectional project. Wooldridge, unlike many, distinguishes between (covariance) stationarity and weak dependence. He says that both are important and that neither necessarily implies the other.
The problem: most people seem to treat these as if they were the same and, in particular, they say that the various tests for unit roots in Stata (my program of choice) are equivalent to checking for stationarity, but as I read Wooldridge, that would only test for weak dependence, more or less.
I can think of ways to look at cov. stat. on my own, but I wonder if there is a formal test for it. Also, I wonder if anyone who has a deep sense of what these terms mean could tell me whether most analysts are in error by only performing unit root tests.
[Edit: Wooldridge, though often helpful, is also often simply unclear. Upon closer inspection of my notes, I found that he did say [Introductory Econometrics, p. 402] that stationarity is not crucial, while weak dependence is, but he doesn't really clarify what he means when he says that it is important, but not crucial].