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Topic: Nonlinear Functions of Unit Roots
Replies: 0

 G. Schroeer Posts: 1 Registered: 12/18/04
Nonlinear Functions of Unit Roots
Posted: Jul 15, 1996 6:23 AM

Hi folks,

suppose we have

x(t)=b*x(t-1)+u(t), t=1,...T

where u(t) is an iid(0,1)-process. Consider

S=\sum_{i=1}^T g(x(t))*v(t)

where g(.) is a function and v(t) is another iid(0,1) process independent of
u(t). For |b|<1 and plim ((sum_{i=1}^T g(x(t))^2)/T ) =q , we have

S/\sqrt(T) \to N(0,q^2).

What is if b=1, that is the unit root case? If g(z)=z, we have the usual
superconsistency results based in Brownian Motions, i.e. mixed gaussian
distributions. But if g(.) is an arbitrary function? I suppose that S
standardized by an appropriate factor is further mixed gaussian. Can someone
give me an answer or some literature for this problem?

Gunar SchrÃ¶er
Institute for Statistics and Econometrics
University of Hamburg
von Melle Park 5
20146 Hamburg
Germany