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

 From Johannes Muck To statalist@hsphsun2.harvard.edu Subject AW: AW: RE: RE: st: Unit roots in non linear regression models Date Sun, 13 Feb 2011 13:38:33 +0100

```Thank you very much Syed and Nick for your quick replies.

I have searched through a couple of econometrics textbooks, including books
on nonlinear time series analysis. However I could not find information on
the theory of nonlinear cointegration.

Do you happen to know some literature that deals with that kind of problem?

Thanks,

Johannes Muck
Düsseldorf Institute for Competition Economics

-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Syed Basher
Gesendet: Freitag, 11. Februar 2011 12:12
An: statalist@hsphsun2.harvard.edu
Betreff: Re: AW: RE: RE: st: Unit roots in non linear regression models

Hi Johannes,

You have asked three questions. My answers are in boldface (don't know if
they
satisfy you):

- Whether the spurious regression problem due to integrated time series is
also a problem with nonlinear regression models

>> Yes, if xt and yt are I(1), that is unit root, they matter for both
linear and
>>non-linear models.

- If the answer is yes: how can I test whether spurious regression is a
problem in my nonlinear model?

>> If you suspect a non-linear relationship, why not check for the existence
of a
>>non-linear cointegration? I don't know whether Stata has a routine for
this, but
>>I know you can obtain a code in Gauss. From the definition of your
variables, it
>>appears that a long-run relationship is possible.

- If spurious regression is a problem in my model: what are possible
remedies?

>> Simple, check the economic theory behind your model.

Hope this helps.

Syed Basher
Qatar National Food Security Programme

----- Original Message ----
From: Johannes Muck <Johannes.Muck@dice.uni-duesseldorf.de>
To: statalist@hsphsun2.harvard.edu
Sent: Fri, February 11, 2011 1:35:30 PM
Subject: AW: RE: RE: st: Unit roots in non linear regression models

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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