Autoregression is more general than the (discretized) Ornstein Uhlenbeck process. For a start, a discretized version of the Ornstein- Uhlenbeck is just an AR(1) process X(n+1) = X(n) + a (X(n) - mu) + error(n+1), but with the coefficient a restricted to 0 < a < 1. This restriction is necessary as the OU process is continuous and reverts to its mean mu.
You can get a translation between the coefficients of an OU process and an AR process by just equating coefficients on like terms. This shouldn't be more difficult that a bunch of linear equations. On Mar 10, 11:06 am, markle...@verizon.net wrote: > 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-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. > > [[alternative HTML version deleted]] > > ______________________________________________ > r-h...@r-project.org mailing listhttps://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
