[R] mean reverting model

markleeds at verizon.net
2009-03-10T00:06:28Z

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
>
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> <http://www.R-project.org/posting-guide.html> and provide commented,
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