[R] AR(1) with an error term arima.sim parameter question
Rolf Turner
r.turner at auckland.ac.nz
Thu Dec 11 09:29:14 CET 2014
On 11/12/14 20:09, Michael Selevan wrote:
> This makes sense, thank you for the thorough response!
>
> One follow up question though. Would your #2 option be the same as, say,
> not using the rand.gen at all and providing the following parameters
> instead?
>
> y3 <- arima.sim(n=10, list(ar=0.8), innov=rnorm(10, sd=0.2))
No. This will call rand.gen=rnorm() to generate innov.start, so
start.innov will be generated with a standard deviation of 1 rather
than 0.2.
>
> or even
>
> y4 <- arima.sim(n=10, list(ar=0.8), innov=rnorm(10, sd=0.2),
> innov.start=rnorm(10, sd=0.2))
Why didn't you try it? It gives an error, saying start.innov is too
short. It needs to be of length *28* according to the error message.
Note that "innov.start" should read "start.innov". My bad;
I got the argument name wrong (on the second attempt!) in my previous
posting.
y4 <- arima.sim(n=10, list(ar=0.8), innov=rnorm(10, sd=0.2),
start.innov=rnorm(28, sd=0.2))
should I think be the same as y2. ***You*** try it and see!
(Set a seed prior to each calculation; that's what seeds are for!)
cheers,
Rolf Turner
<SNIP>
> On Wed, Dec 10, 2014 at 1:04 PM, Rolf Turner <r.turner at auckland.ac.nz
> <mailto:r.turner at auckland.ac.nz>> wrote:
>
>
> Please see below.
>
>
> On 10/12/14 20:21, Michael Selevan wrote:
>
> Hello,
>
> I am attempting to plot an AR(1) model with a standard deviation
> and I am a
> little confused as how to do that. I have been looking through the
> interwebs and some documentation and I see that there is
> potentially a few
> different ways to do this.
>
> First, simply using the documentation I came up with the command
>
> arima.sim(n=10, list(ar=0.8), innov=rnorm(10, sd=0.2))
>
> which would give me the standard deviation I want. Or I believe
> that to be
> the case. However, after some more searching and googling, I saw
> an example
> where someone used this as a means of adding the AR error term
>
> error.model=function(n){rnorm(__n, sd=0.2)}
>
> y = arima.sim(n=10, list(ar=0.8), innov=rnorm(10, sd=0.2), rand.gen=
> error.model)
> Now, I am a little confused by this. Would having the error term
> in the
> innov parameter as well as the rand.gen be redundant? What would
> be the
> expected differences between the two? Should only 1 be used?
>
> Just looking for some clarification. Been searching and havent
> found too
> many examples that explicitly state how to add the error term to
> an AR(1)
> model.
>
>
> It's a little bit subtle, but in a way that's not too important.
>
> There is, in addition to "innov" a starting innovations vector
> "start.innov" that is needed. If either innov or start.innov is not
> supplied their values get supplied by rand.gen(). So in your second
> call to arima.sim() ***start.innov*** is being supplied by rand.gen()
> (but ***innov*** will be taken to be equal to the argument supplied.
>
> In your first call, where rand.gen() is not specified (and start.innov
> is not specified), the supplied value of innov will be used and
> start.innov will be produced by the *default* value of rand.gen()
> which is rnorm(), you'll get rnorm(n.start,0,1).
>
> Thus in your first call, the starting innovations will be done with
> a different standard deviation than the other innovations. Which is
> probably not what you want.
>
> Hence the second call is correct --- but it *is* kind of redundant
> and confusing to supply "innov" as well as rand.gen(). The code
> would be
> clearer if "innov" were dispensed with and it was just left to
> rand.gen() to do the work.
>
> The following is not important, but it might be mystifying: If you
> leave out "innov" you will get a different result --- even if you
> set a seed for the random number generators a priori. E.g.:
>
> # 1.
> set.seed(42)
> innov <- rnorm(10,0,0.2)
> error.model=function(n){rnorm(__n, sd=0.2)}
> y1 <- arima.sim(n=10, list(ar=0.8), innov=innov,
> rand.gen=error.model)
>
> # 2.
> set.seed(42)
> error.model=function(n){rnorm(__n, sd=0.2)}
> y2 <- arima.sim(n=10, list(ar=0.8),rand.gen=error.__model)
>
> The vectors y1 and y2 are (surprisingly until you think carefully)
> different.
>
> This is because for y1, innov.start is generated *after* innov is
> generated, whereas for y2 innov.start is generated *before* innov is
> generated. The first entry of innov for y1 will be the same as the
> first entry of innov.start for y2. So the sequence of innovations is
> different.
>
> Bottom line: I would recommend *not* using the "innov" argument and
> just specifying rand.gen() to get the standard deviations that you want.
>
> HTH
>
> cheers,
>
> Rolf Turner
>
> --
> Rolf Turner
> Technical Editor ANZJS
>
>
>
>
> --
> J. Michael Selevan
--
Rolf Turner
Technical Editor ANZJS
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