i think there's confusion here between a time series that reverts to its long term mean and an "ornstein uhlenbeck" type of mean reversion. they're not the same thing and I don't want to go into the difference because I would probably just add to the confusion.
you might be better off sending your original question to the R-Sig-Finance list although you may have already because I saw something abiout the same topic earlier ? If you google for ornstein uhlenbeck, there should be something somewhere on the net that shows that a discrete version of an ornstein uhlenbeck is think a an AR(2) with some complex parameters which are functions of the volatility and mean reverting parameter of the continuous OU process. I googled earlier because I was going to send it to you but the site where I wanted to go was busy. I think it's called planetmath.org or something like that. On Mon, Mar 9, 2009 at 7:54 PM, andrew wrote: > Autoregression is just X(n+1) = a X(n) + b + error. The mean reverting model is when |a| < 1. Estimation is carried out using x_ar <- ar(x) summary(x_ar) standard error is found in the square root of the diagonal of the x_ar $asy.var.coef matrix. please read the documentation found at ?ar to get full details. On Mar 10, 9:18 am, Josuah Rechtsteiner <rechtstei...@bgki.net <mailto:rechtstei...@bgki.net>  <mailto:rechtstei...@bgki.net> > wrote: > hi andrew, > > the problem is that I don't know what kind of model this exactly is... > I only know that I have to do it this way and how the model is  > structured. > > > >> Mean reverting model = autoregression?  If so, then search for > >> ?ar > >> or > >> ?arima > >> to fit a time series. > >> On Mar 10, 4:36 am, Josuah Rechtsteiner <rechtstei...@bgki.net >> <mailto:rechtstei...@bgki.net>  <mailto:rechtstei...@bgki.net> > >> wrote: >>> dear useRs, > >>> i'm working with a mean reverting model of the following  >>> specification: > >>> y = mu + beta(x - mu) + errorterm, where mu is a constant > >>> currently I estimate just y = x (with lm()) to get beta and then >>> calculate mu = estimated intercept / (1-beta). > >>> but I'd like to estimate mu and beta together in one regression-step >>> and also get the test-statistics (including parameter variance) for >>>  >>> mu >>> as well as for beta in the summary of the regression. > >>> could you please help me? > >>> thanks very much in advance! > >>> josuah > >>> ______________________________________________ >>> r-h...@r-project.org <mailto:r-h...@r-project.org>  >>> <mailto:r-h...@r-project.org>  mailing >>> listhttps://stat.ethz.ch/mailman/ <https://stat.ethz.ch/mailman/>  >>> <https://stat.ethz.ch/mailman/> listinfo/r-help >>> PLEASE do read the posting >>> guidehttp://www.R-project.org/posting-guide.html >>> <http://www.R-project.org/posting-guide.html>  >>> <http://www.R-project.org/posting-guide.html> and provide commented, >>> minimal, self-contained, reproducible code. > >> ______________________________________________ >> r-h...@r-project.org <mailto:r-h...@r-project.org>  >> <mailto:r-h...@r-project.org>  mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> <https://stat.ethz.ch/mailman/listinfo/r-help>  >> <https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the >> posting guidehttp://www.R-project.org/posting-guide.html >> <http://www.R-project.org/posting-guide.html>  >> <http://www.R-project.org/posting-guide.html> and provide commented, >> minimal, self-contained, reproducible code. > > ______________________________________________ > r-h...@r-project.org <mailto:r-h...@r-project.org>  > <mailto:r-h...@r-project.org>  mailing > listhttps://stat.ethz.ch/mailman/listinfo/r-help > <https://stat.ethz.ch/mailman/listinfo/r-help>  > <https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the > posting guidehttp://www.R-project.org/posting-guide.html > <http://www.R-project.org/posting-guide.html>  > <http://www.R-project.org/posting-guide.html> and provide commented, > minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org <mailto:R-help@r-project.org>  <mailto:R-help@r-project.org>  mailing list https://stat.ethz.ch/mailman/listinfo/r-help <https://stat.ethz.ch/mailman/listinfo/r-help>  <https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html <http://www.R-project.org/posting-guide.html>  <http://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code. [[alternative HTML version deleted]]
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