Nonparametric cointegration analysis



Cov


6                    x ʃ

(jF (x ) W(x ) dx), (]Fj (y ) W(y ) d'


(A.10)


^Fι(x)Fj(y)min(xjy)dxdy] ■ Iq = O for i j,


Cov


6 . x ,                   - xï

Fi (x ) W(x ) dx], (Fj(1) W(1) -ʃfj (y ) W(y ) dy] ,


F   (1FxFi(x ) dx ʃ ʃʃF (x )fj (y)min(x ,y ) dxdy] ’ 1q


(A.11)


Cov


ʃ Fi(y)dy


ï ï

dx

J J


O for ij ,


6

jF1 (1) W(1) - ʃfi(x) W(x)a⅛j, (Fj(1) W(1) - ʃf (y) W(y)dyj ^


= (f∕1)Fj(1) - F1 (ɪ)ʃf(x)dx F Fj(1)∫f (x)dx


F (-Fi(1)Fj(1) + F1 (1)∫Fj(x)dx +


y × 1q

Fj(1)Fi (x) dx

y × Iq


(A.12)


Q.E.D.


= (ʃʃk(x)fj(y)min(xX')dxdy f Fi(1)Fj(I)J × Iq
ʃ ʃF.(x)F.(x)dx × Iq= O for i j.


Proof of Lemma 2: Let F be a typical function Fk, with derivative f, and let ξ be a cointegrating
vector. Using Lemma 9.6.3 in Bierens (1994, p.200) it follows now that


39




More intriguing information

1. Testing Hypotheses in an I(2) Model with Applications to the Persistent Long Swings in the Dmk/$ Rate
2. Conservation Payments, Liquidity Constraints and Off-Farm Labor: Impact of the Grain for Green Program on Rural Households in China
3. Does South Africa Have the Potential and Capacity to Grow at 7 Per Cent?: A Labour Market Perspective
4. The name is absent
5. Tobacco and Alcohol: Complements or Substitutes? - A Statistical Guinea Pig Approach
6. The name is absent
7. Outsourcing, Complementary Innovations and Growth
8. Sector Switching: An Unexplored Dimension of Firm Dynamics in Developing Countries
9. Optimal Taxation of Capital Income in Models with Endogenous Fertility
10. A Brief Introduction to the Guidance Theory of Representation