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On the Limit Theory of Mixed to Unity VARs: Panel Setting With Weakly Dependent Errors

Stauskas, Ovidijus LU (2019) In Working Papers
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Working Paper
publication status
published
subject
keywords
Local to Unity, Mildly explosive, Panel;, Weak Dependence, Wald Test, C12, C32, C33
in
Working Papers
issue
2019:2
pages
58 pages
language
English
LU publication?
yes
id
2f26207e-7e6c-465b-91b9-1a489ab631b4
alternative location
https://swopec.hhs.se/lunewp/abs/lunewp2019_002.htm
date added to LUP
2019-01-15 11:31:48
date last changed
2019-01-15 11:31:48
@misc{2f26207e-7e6c-465b-91b9-1a489ab631b4,
  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. },
  author       = {Stauskas, Ovidijus},
  keyword      = {Local to Unity,Mildly explosive,Panel;,Weak Dependence,Wald Test,C12,C32,C33},
  language     = {eng},
  note         = {Working Paper},
  number       = {2019:2},
  pages        = {58},
  series       = {Working Papers},
  title        = {On the Limit Theory of Mixed to Unity VARs: Panel Setting With Weakly Dependent Errors},
  year         = {2019},
}