[R-SIG-Finance] Unit Root Tests: Empirical Results vs Theory

[Matthieu Stigler]

Adams, Zeno a écrit :
> I am currently analyzing a data set using panel cointegration. Like with any other cointegration method the variables have to be non-stationary. For my specific case (German commercial real estate market) I find the variables "total stock of office space" and "vacancy rates" to be non-stationary using standard unit-root tests. 
> >From theoretic considerations however it is clear that the vacancy rate has to be between 0 and 1 and also that the office space is unlikely to wander off to any arbitrary values.
>
> how would you deal with such a situation?
>
> Do you think it is possible to have "technical non-stationarity" in the sense that shocks in the past have a permanent impact on the series but that the variable exhibits a random walk behavior only within certain bounds? If that would be the case then it would be necessary to treat the vacancy rate as a non-stationary variables since ignoring this would lead to spurious regression.
>   
The interesting concept that a variable is non-stationary within  bounds 
and stationary outside (and so globally stationary) can be tested, using 
non-linear unit root tests. There are two of such tests (unit root vs 
stationary threshold autoregressive process) in the dev version of 
package tsDyn: BBCTest() and KapShinTest() 
(http://code.google.com/p/tsdyn/wiki/ThresholdCointegration)

They may be nevertheless not so useful as if you find that the variable 
is indeed globally stationary, you may nevertheless not know what do do 
with it!!

It is not clear and few discussed in the literature whether the fact 
that the variable is globally stationary does not lead to spurious 
regression. Note also that the concept of integrated (I(0) and I(1)) 
time series is not well defined in the case of non-linear time series 
(see Gonzalo and Pittarakis threshold effect in cointegrating 
relationships 2006).

Mat
> Thank you for your contributions
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