Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/260272 
Year of Publication: 
2019
Series/Report no.: 
Working Paper No. 2019:2
Publisher: 
Lund University, School of Economics and Management, Department of Economics, Lund
Abstract: 
In this paper we re-visit a recent theoretical idea introduced by Phillips and Lee (2015). They examine an empirically relevant situation when multiple time series under consideration exhibit different degrees of non-stationarity. By bridging the asymptotic theory of the local to unity and mildly explosive processes, they construct a Wald test for the commonality of the long-run behavior of two series. Therefore, a vector autoregressive (VAR) setup is natural. However, inference is complicated by the fact that the statistic is degenerate under the null and divergent under the alternative. This is true if the parameters of the data generating process are known and re-normalizing function can be constructed. If the parameters are unknown, as is in practice, the test statistic may be divergent even under the null. We solve this problem by converting the original setting of one vector time series in a panel setting with N individual vector series. We consider asymptotics with fixed N and large T and extend the results to sequential asymptotics when T passes to infinity before N. We show that the Wald test statistic converges to nuisance parameter-free Chi-squared distribution under the null hypothesis.
Subjects: 
Local to unity
mildly explosive
panel
weak dependence
Wald test
JEL: 
C12
C32
C33
Document Type: 
Working Paper

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