Nonparametric cointegration analysis

nξ ξ TMnz ( F) ξ ξ IF(1)

snw(1)
nn

(A.13)

.. „ /-f c

^ξ T⁽z0 - ^w 0⁾Vn F⁽¹⁾ - Jf^x⁾

Note that

F(1) -jxf(x ) dx = ʃF(x ) dx = 0,
hence

F⁽¹⁾ - ʃInxlf(x⁾^dx∖ ≤ 1 f_x^fx⁾|dx
^J n ⁿ J

[^nx ] _dx 1
n

(A.14)

(A.15)

and consequently equation (A.13) then becomes

nξ ξ TMnz ( F) - ξ ïF(1)

Sn^w(1)
nn

- ʃfx) S^ dx 1
nn ^

(A.16)

Moreover,

ξTS∆(x) - ξ⅛∙_m - ξTw0. (A'¹⁷⁾
and consequently

ⁿ^ξ^τ^m^δ⁽F) = ^ξ⁷(F(¹)(^w_n~^w0) - ʃʃ(^x⁾⁽^w[_nx] ~^w0)^dx]

(A.18)

^{ξ ξ} ^F⁽¹⁾^W_n - f/(.x )^W [ _nx ] ^dx) = F(¹) ^ξ Tw_n ^{+ θ}p ⁽¹⁾-

The last equality in (A.18) follows from the fact that by the dominated convergence theorem,