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# RE: RE: RE: st: Unit roots in non linear regression models

 From Nick Cox To "'statalist@hsphsun2.harvard.edu'" Subject RE: RE: RE: st: Unit roots in non linear regression models Date Fri, 11 Feb 2011 10:41:21 +0000

```It sounds as if you have a clear idea of what the generating processes might be. Given that, one of the best ways to establish whether you get a problem, and more importantly how big it is, in the nonlinear case is by simulation.

Nick
n.j.cox@durham.ac.uk

Johannes Muck

I will try to clarify my question:

If we go back to the linear case and look at two random variables, say y and
x, both of which are independent I(1) processes so that:

y_t = y_t-1 + a_t

and

x_t = x_t-1 + e_t

with a_t and e_t being i.i.d. innovations with mean zero and constant
variances.

If I run a regression of y_t on x_t this will often result in a significant
coefficient for x although there is no relationship between  y and x
(spurious regression problem).

My main question now is whether this problem carries over to the nonlinear
case, so that in my nonlinear regression model the coefficients a1 - a4 and
b0 - b2 are estimated to have a significant impact on y although in reality
they don't.

My two questions posted earlier refer to this question.

In particular I would like to know:

- Whether the spurious regression problem due to integrated time series is
also a problem with nonlinear regression models
- If the answer is yes: how can I test whether spurious regression is a
problem in my nonlinear model?
- If spurious regression is a problem in my model: what are possible
remedies?

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```