Nonparametric cointegration analysis



corresponding to the r zero eigenvalues. Then:

Lemma 2. Under Assumption 3 and the conditions of Lemma 1,

         ^ï

RrTD (1) Y1 ^F1(x)2dx


Fk(1)RrτD,Z


RrM(!) ft

RM z (Fk) n

V k 7

jointly in k = 1,...,m, where the Yk ’s andZ are independent q-variate standard normally
distributed, with Y
k defined by (13). Moreover, Z does not depend on Fk .

Such weight functions Fk do exist. In particular,

Lemma 3. If Fk(x) = cos(2kπx), then the conditions (6) through (10) hold. Moreover, we then

have Fk(1) = 1, ʃʃFk(x)Fk(y)min(xy) dxdy = 1(kπ y2, ʃFk(x)2dx = 1.

There are many ways to choose these functions Fk, but as will be shown in section 5, the
above choice is optimal in some sense.

Denoting

Fk(x )2 dx


γ k =            j

y ^^I^k(x )Fk((y )min(x, y ) dxdy


, δk


Fk (1)

ʃFk (x )2 dx


(14)


it follows now easily from Lemmas 1-2:



More intriguing information

1. Constrained School Choice
2. Locke's theory of perception
3. RETAIL SALES: DO THEY MEAN REDUCED EXPENDITURES? GERMAN GROCERY EVIDENCE
4. The Impact of Individual Investment Behavior for Retirement Welfare: Evidence from the United States and Germany
5. Innovation Trajectories in Honduras’ Coffee Value Chain. Public and Private Influence on the Use of New Knowledge and Technology among Coffee Growers
6. The name is absent
7. Restricted Export Flexibility and Risk Management with Options and Futures
8. A multistate demographic model for firms in the province of Gelderland
9. The Triangular Relationship between the Commission, NRAs and National Courts Revisited
10. Regional science policy and the growth of knowledge megacentres in bioscience clusters