Nonparametric cointegration analysis

.. „            /-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

and consequently equation (A.13) then becomes

Moreover,

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

^{n ξτmδ(}F) = ^ξ7(F(¹)(^w_n~^w0) - ʃʃ(^x)(w[_nx] ~^w0)^dx]

^{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,

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