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)) or even y4 <- arima.sim(n=10, list(ar=0.8), innov=rnorm(10, sd=0.2), innov.start=rnorm(10, sd=0.2)) Would either of these then be the same result as your option #2? Thanks again! On Wed, Dec 10, 2014 at 1:04 PM, Rolf Turner <r.tur...@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 [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.