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

 From Nick Cox To "'statalist@hsphsun2.harvard.edu'" Subject st: RE: RE: Unit roots in non linear regression models Date Thu, 10 Feb 2011 12:10:40 +0000

```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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