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

[Johannes Muck <Johannes.Muck@dice.uni-duesseldorf.de>]

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?

Thanks,

Johannes Muck

-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Nick Cox
Gesendet: Donnerstag, 10. Februar 2011 13:11
An: 'statalist@hsphsun2.harvard.edu'
Betreff: st: RE: RE: Unit roots in non linear regression models

I see that the b_i could have differing signs, but my main point remains
similar. 

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

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
Sent: 10 February 2011 11:57
To: 'statalist@hsphsun2.harvard.edu'
Subject: st: RE: Unit roots in non linear regression models

I don't understand this at all. If your main idea about dynamics is that of
exponential decline, your series can hardly be stationary. The two parts of
your question appear to be contradictory. Perhaps you mean something more
specific, such as stationarity of some error term, but please clarify. 

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

Johannes Muck

I would like to estimate a nonlinear regression model of the form

y_it = a_i*(1 - exp(-b_i*t))

whereby 

a_i = exp(a1*x1 + a2*x1^2 + a3*x2 + a4*x3)

and

b_i = b0 + b1*z1 + b2*z2


The economic interpretation of the model is as follows: y_it denotes company
i's market share in period t, a_i denotes company i's long-term market
share, and b_it represents company i's speed of convergence towards its
long-term market share.
y_it is observed for 129 companies for 63 periods on average. 

I tested whether each of the 129 time series exhibits a unit root using the
command 

-by company, sort: kpss y- 

the test strongly suggests that most of the 129 time series exhibit a unit
root.

I have two questions:

1) Can standard unit-root tests be applied although I am estimating a
nonlinear model?

2) Is there a possible remedy for the non-stationarity of y_it? From my
intuition I would say that using first-differencing will be no use in the
nonlinear case.

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