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From |
"Clive Nicholas" <clivelists@googlemail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Constant terms in AR1 error regressions |

Date |
Thu, 18 Dec 2008 14:43:27 +0000 |

Michael Hanson replied: > An "error regression equation" is a little ambiguous: after all, the errors > are unobservable (and thus cannot be "put" into a regression), while the > residuals are by construction mean zero, so a constant term is unnecessary. > Although you could run a regression on the residuals of a previously > estimated model (and many tests of serial dependence have that form), > typically what one does is model the (assumed) auto-regressive properties of > the error term as part of the specification to be estimated -- in a > univariate or single-equation context, this can be accomplished in Stata > with the -arima- command. I was pressed was for time when posting this query, so apologies for using the wrong terminology: I did, of course, mean 'residuals'. Although you say a constant term in such residual-on-residual regressions are unnecesary, a constant term nevertheless appears, and my task is to do this in -reg-, not -arima-. Essentially, what I'm asking is is it best to leave it there or to apply the -nocons- option? > Also, note that u_{0} is the initial observation in time of the > (hypothetical) u time series, u_{t} for t = 0, \dots, T. It is not a > parameter to be estimated (like a constant). When I wrote u_{0} in this equation, I meant this to represent the constant term, since it appears in all of the residual-on-residual equations I have run in Stata. > I'm not certain what literature you are referring to, but I know from > teaching time series that textbooks often do not clearly distinguish > hypothetical concepts from specifications that can be estimated on "real" > data. > > By the way, if you are estimating an AR(1) model on "real" data (not > residuals), you will certainly want to include a constant term. Whether it > is of interest or not depends in part on your application. But its > exclusion is likely to yield biased estimates of the other parameters (such > as \rho), just as in the OLS case. Thanks for this. -- Clive Nicholas [Please DO NOT mail me personally here, but at <clivenicholas@hotmail.com>. Please respond to contributions I make in a list thread here. Thanks!] "My colleagues in the social sciences talk a great deal about methodology. I prefer to call it style." -- Freeman J. Dyson. * * 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**:**Re: st: Constant terms in AR1 error regressions***From:*Michael Hanson <mshanson@mac.com>

**References**:**st: Constant terms in AR1 error regressions***From:*"Clive Nicholas" <clivelists@googlemail.com>

**Re: st: Constant terms in AR1 error regressions***From:*Michael Hanson <mshanson@mac.com>

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