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Nonlinear Functions of Unit Roots
Posted:
Jul 15, 1996 6:23 AM


Hi folks,
suppose we have
x(t)=b*x(t1)+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?
Thank you in advance
Gunar SchrÃ¶er Institute for Statistics and Econometrics University of Hamburg von Melle Park 5 20146 Hamburg Germany



