[R] AR(1) with an error term arima.sim parameter question

[Michael Selevan]

Thanks for all the help! Ill give them a shot and compare the results.

On Thu, Dec 11, 2014 at 12:29 AM, Rolf Turner <r.turner at auckland.ac.nz>
wrote:

> 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
>



-- 
J. Michael Selevan

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