Nonparametric cointegration analysis

JJexp(2 i π j ₁ x )exp(2 i π j ₂ y )min(x, y ) dxdy
x

= ∣exp(2 i π j ₁ x)ʃy exp(2 i π j₂y)dydx - ∣x exp(2 i πj ₁ x)∣exp(2 i π j₂y)dydx

^{x ex}p⁽² i^π (j'i +j2)^x)       ʃ ^exp⁽² i^π (j'i +j2)^x)       ʃ ^exp⁽² i^{π j}i x)

______________dx ʃ I__________LJ___dx + I_________¹__dx

^{2 i π j} 2              2      (2 i ∏ j 2)²           2 (2 i π j 2)²

ʃx ^exp⁽² i^π (j' 1 +j2) x⁾ ʃx^exp⁽² i^π j 1 x⁾

- I____________LJ___dx + I___________¹__dx

2       2 i π j 2             2     2 i π j 2

₌ _    1     ₊ ¹(j' 1^+j 2⁼⁰⁾

^{4 π 2}j 12      4 π²j ²

and

It follows now from (A.38) and (A.42) that

∞

V

∞

λ.¹

and it follows from (A.38) and (A.43) that

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