Lina,
check ?density (and do so carefully). R uses a kernel estimate, by default
"Gaussian" if I remember correctly. Values in a certain grid can be found from
the code I sent earlier. I didn't check, but these are most likely just
linearly interpolated by plot.density, and as the grid is sufficiently tight,
it visually looks smooth. You could mimick this by linearly interpolating from
the two closest neighbours for any "new" x values (or, as a rough
approximation, choosing the density value of the nearest neighbour). I am not
sure whether there are some specificities for time series in general or GARCH
models in particular, that's not my area of expertise. Maybe there is some
method for GARCH objects in the library you are using (you don't tell me which
one). Try
str(density(x))
from your original post to see whether you might have to adapt the proposed way
to get these values. I copy the list in case someone can give more details on
that.
Two side remarks:
* You should note that the "density" function in R takes a lot of parameters
that might heavily influence the outcome, and even though R will propose some
defaults that will work frequently, they might not be optimal or even
appropriate for your particular situation, model, and data.
* From your messages I fear that you have a limited understanding of the notion
of density functions, at least for continuous distributions; they do NOT give
the probability that a certain value is taken. Try
plot(x<-seq(-1,1,0.01), dnorm(x, sd=.25), type="l")
to see that the density can easily exceed 1 and can hence not represent a
probability. In fact, the theoretical probability that a specific value is
actually taken from a continuous distribution is always equal to 0.
I would strongly suggest to contact a local statistician to clarify these
issues.
HTH, Michael
________________________________
From: Lina Rusyte [mailto:liner...@yahoo.co.uk]
Sent: Dienstag, 29. September 2009 18:03
To: Meyners,Michael,LAUSANNE,AppliedMathematics
Subject: RE: [R] Probability of data values form DENSITY function
Dear Mr. Michael Meyners,
Assume, that I have simulated data from GARCH process:
spec = garchSpec(model = list(omega = 0.01, alpha = 0.13, beta = 0.86,
shape = 6), cond.dist = "std")
yt<-garchSim(spec, n = 4000)
The empirical distribution of this data (yt) is assumed to be not
parametrized distribution). This data is my in-sample data.
I have another set of the data (yt1), generated from the same process
(but it is not the same as yt). I need to find the probabilities of these data
(yt1) points in previously mentioned empiric distribution (of yt).
Simply to say, having continuous EMPIRIC density function, I need for
some points in x axis (values) to find out the corresponding values of y axis
(their probability).
R plots empiric density function, so I assume it approximates somehow
the empirical density function.
Thank a lot for the help in advance.
Best regards,
Lina
--- On Tue, 29/9/09, Meyners,Michael, wrote:
From: Meyners,Michael,LAUSANNE,AppliedMathematics
Subject: RE: [R] Probability of data values form DENSITY
function
To: "Lina Rusyte" <liner...@yahoo.co.uk>
Cc: "R help" <r-help@r-project.org>
Date: Tuesday, 29 September, 2009, 4:59 PM
Lina, check whether something like
data.frame(density(rnorm(10))[1:2])
contains the information you want. Otherwise, try to be (much)
more specific in what you want so that we do not need to guess (and of course
provide minimal, self-contained, reproducible code). That has a higher chance
to trigger some responses than posting the same message again. And if you even
explain what you want to do with these values, you might get even better
responses.
HTH, Michael
> -----Original Message-----
> From: r-help-boun...@r-project.org
<http://de.mc256.mail.yahoo.com/mc/compose?to=r-help-boun...@r-project.org>
> [mailto:r-help-boun...@r-project.org
<http://de.mc256.mail.yahoo.com/mc/compose?to=r-help-boun...@r-project.org> ]
On Behalf Of Lina Rusyte
> Sent: Dienstag, 29. September 2009 16:45
> To: R help
> Cc: R help
> Subject: [R] Probability of data values form DENSITY function
>
> Hello,
> Â
> Could someone help me please and to tell how to get the
> probability from empirical DENSITY (not parametric) for each
> data value (R function).
> For example, for normal distribution there is such a function
like:
> Â
> “dnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p =
> FALSE)† I need the same function only for the empiricalÂ
DENSITY function (which does not correspond to any typical >
distribution).
> R plots the density function of any data:
> Â
> “plot(density(x))â€
> Â
> I need to find out the probability for each data value from
> this plot-line.
> Â
> Best regards,
> Lina
>
>
>
> [[alternative HTML version deleted]]
>
>
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