Nonparametric cointegration analysis



7. Cointegrating systems with unconstrained drift

7.1. Non-seasonal drift

Until so far all our derivations were based on the assumption that the drift parameter
vector μ is orthogonal to the cointegrating vectors. Cf. Assumption 3. The problem is that
without Assumption 3 the result of Lemma 2 no longer holds, due to the fact that

Σn=11cos(2kπt/n) = n/2, although Σnt=1cos(2kπt/n) = 0, so that, with Fk(x) = cos(2kπx), the result
of Lemma 2 now becomes:

RM(Ft√n - 1rμ.-'

RM (Fk) n
                k

(          __________'

1CD (1) Yk ftFk(x )2dx

`    Fk(1)R,TD,Z

and consequently, part (15) of Lemma 4 becomes:


D

RC-A R
m


(

ɪ _

RqT-rC(DE XkXkTC(1)TR,-t

k- 1

m _

RrT μ∑ XkTC (1)R

F               k1


'

RTCd)∑ Xt μ tr
-,

Rr μμtR


Clearly, this will render all our test results invalid. However, a minor change of the functions
Fk will cure the problem:


Lemma 8. Let Fn,k(x) = cos[2kπ(nx - ½)/n] and Fk(x) = cos(2kπx). Then


nn

Fnk (t (t/n ι = tLk(τ/.)( t/n 1 = 0,

t=1                            t-1


(38)


and


lim n sup F^nk(x) - Fk(x) = kπ .
n -∞ 0x1     ’


(39)


23




More intriguing information

1. The name is absent
2. Methods for the thematic synthesis of qualitative research in systematic reviews
3. The Employment Impact of Differences in Dmand and Production
4. Outline of a new approach to the nature of mind
5. Tax Increment Financing for Optimal Open Space Preservation: an Economic Inquiry
6. SOCIOECONOMIC TRENDS CHANGING RURAL AMERICA
7. Stable Distributions
8. The name is absent
9. The value-added of primary schools: what is it really measuring?
10. The mental map of Dutch entrepreneurs. Changes in the subjective rating of locations in the Netherlands, 1983-1993-2003
11. Howard Gardner : the myth of Multiple Intelligences
12. Implementation of Rule Based Algorithm for Sandhi-Vicheda Of Compound Hindi Words
13. Les freins culturels à l'adoption des IFRS en Europe : une analyse du cas français
14. A multistate demographic model for firms in the province of Gelderland
15. The name is absent
16. The name is absent
17. Errors in recorded security prices and the turn-of-the year effect
18. A Bayesian approach to analyze regional elasticities
19. The Formation of Wenzhou Footwear Clusters: How Were the Entry Barriers Overcome?
20. Effort and Performance in Public-Policy Contests