Nonparametric cointegration analysis

where the X^*_i’s are i.i.d. N_q-r(0,I_q-r), and the latter minimum solution is equal to, and bounded
from below by

m

LM

m

m

^кk1

ï

T λ. RTC(1)C(1)TR, ).

mιn∖ q ^{r v 7} V ^{7    ,}q-rf

7

This proves the inequality involved. Since

m +1

V

√

(A.52)

and M_α,s,q-r,m is decreasing in m, it follows now that the right-hand side lower bound involved
increases with m. Q.E.D.

Proof of Lemma 8: For k > 0 we can write

n

2J2 t cos(2kπ (t-0.5)/n) = g_n(2kπ /n) + g_n(-2kπ /n),
where

47

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