Modified KPSS Tests for Near Integration - Department of ...

That ^! 2 c
and so
p
! ! 2 follows simply by noting that, for t = 2; :::; T we can write
yt c;T yt 1 = t + (c c)T 1 wt 1
rc;t = t + (c c)T 1 wt 1
= t + op(1):
P T
t=2 f t + (c c)T 1 wt 1g
(T 1)
To show the second part of the Theorem note that when c = c > 0 we have, for t = 2; :::; T ,
rc;t = (wt c;T wt 1) mc;w
mc;w =
= vt mc;w;
=
P T
t=2 (wt c;T wt 1)
P T
t=2 vt
(T 1)
so rc;t invariant to and using standard results
[rT ]
(T 1)
T 1=2
X
rc;i ) ![W (r) rW (1)]:
i=2
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