Nonparametric cointegration analysis

and

V tz ∙ = z dLŸ ,'..!L .2,/1 - i ^cos(^kπ /ⁿ ) 1
t! dz⅛ z-1 ² ^ sin(kπ /n) ,

Thus, taking the real part, we have

nn

COs cos(2kπ t/n) о 0,      t cos(2kπ t/n) = 1 n,

t= 1                                             t-1                                       ²

which proves the conditions (6) and (7). The other condition follow from the proof of Lemma
6 below. Q.E.D.

Proof of Lemma 4: We only prove (17); the other parts of Lemma 4 follow straightforwardly
from Lemmas 1-2. It is a standard exercise in linear algebra to verify that

where

= -n (RTÂ R )1( nRTÂ R )(л²²/n²) = (Л21)^T

^q q m m q-r' ^{q q r} m r'^q m ^{7 v}m⁷

Therefore,

42

<<   39   40   41   42   43   44   45   >>

More intriguing information