CES VŠEM o aktuálních ekonomických problémech

unit roots specified as a standard AR(1) process that is common
for all units ( ) in a panel or individual non-stationary processes
under the null hypothesis; however, the alternative for individual
pURTs differs. 37
To begin with, let us assume a standard autoregressive process
(AR(1)) in the panel context can be expressed as follows (see
Stata, 2009):
(11)
where is a particular time series, represents the fixed
effects, is a term that may contain a linear time trend or
panel specific means, is the parameter of an autoregressive
process, is a error term, is the cross-section
dimension,
is the time dimension.
The equation (11) can be transformed into the following form:
(12)
Standard pURTs are employed to the individual time series ( )
and work with the null hypothesis being tested ( ) in the form:
and with the alternative hypothesis ( )
In the case of the equation (12), the null is (
alternative ( ). 38
(13)
(14)
), the
Regarding individual pURTs, we focus on selected test of the first
generation. One of the oldest is the Lin-Levin-Chu test (Levin al.,
37 For a review of early and more recent methods and their discussion
see e.g. Banerjee, 1999 or Breitung and Pesaran, 2008.
38 Only the Hadri LM test (see below) is based on the opposite of this, i.e. the
null hypothesis assumes stationarity.
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