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From |
Syed Basher <syed.basher@yahoo.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: AW: RE: RE: st: Unit roots in non linear regression models |

Date |
Fri, 11 Feb 2011 03:12:02 -0800 (PST) |

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. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**AW: AW: RE: RE: st: Unit roots in non linear regression models***From:*Johannes Muck <Johannes.Muck@dice.uni-duesseldorf.de>

**References**:**st: Unit roots in non linear regression models***From:*Johannes Muck <Johannes.Muck@dice.uni-duesseldorf.de>

**st: RE: Unit roots in non linear regression models***From:*Nick Cox <n.j.cox@durham.ac.uk>

**st: RE: RE: Unit roots in non linear regression models***From:*Nick Cox <n.j.cox@durham.ac.uk>

**AW: RE: RE: st: Unit roots in non linear regression models***From:*Johannes Muck <Johannes.Muck@dice.uni-duesseldorf.de>

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