Nonparametric cointegration analysis

JxFk(x)dx о 0,                                                                       ⁽²⁸⁾

respectively, and to verify afterwards that the optimal weight functions F_k satisfy the stronger
conditions (6) and (7).

Without loss of generality we may represent the functions F_k by their Fourier flexible
form

∞∞

Fk^(x) ^{α α}o,k ⁺ ∑ ^αj,k^cos(2jπx) ⁺ ∑ ^β_j,k^sin(2jπx)

Then by some tedious but straightforward calculations it can be shown that:

Lemma 6. The conditions (27), (28), (8), (9), and (10) now read as:

Fk^(χ)d^{χ α α}ok - ⁰

Combining (1) and the results of Lemma 6, we have

16

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