Re: [R] Null model for arima.sim().

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From: Prof Brian Ripley (
Date: Tue 25 May 2004 - 03:18:05 EST

Message-id: <Pine.LNX.4.44.0405241816170.1986-100000@gannet.stats>

It's not really intended to work, but a small change makes it work.
(1:nstart is wrong for a null model.)

list(ar=numeric(0), ma=numeric(0)) might be a little clearer.

On Mon, 24 May 2004, Rolf Turner wrote:

> In some time series simulations I'm doing, I occasionally want the
> model to be ``white noise'', i.e. no model at all. I thought it
> would be nice if I could fit this into the arima.sim() context,
> without making an exceptional case. I.e. one ***could*** do
> something to the effect
> if(length(model)==0) x <- rnorm(n) else x <- arima.sim(model,n)
> but it would be more suave if one could just use arima.sim() all the
> time.
> Experimenting I found that arima.sim() accepts an empty list as the
> model, e.g.
> x <- arima.sim(list(),100)
> and the result appears to be white noise. There are a couple of
> funnies, but. One is that the resulting x is of length 99, rather
> than 100. The other is that if I do
> set.seed(42)
> x <- arima.sim(list(),101)
> set.seed(42)
> y <- rnorm(100)
> the results are, modulo the order in which they appear, virtually
> identical. But not ***quite*** identical! If I do
> ``sort(x)-sort(y)'' I get zeroes (to 9 decimal places) everywhere,
> except for entries 86 to 90, which are
> [86] -0.013709324 -0.087867933 -0.002327022 -0.015243692 -0.050845101
> Perhaps arima.sim() is not really intended to accept an empty list
> as a model, and the fact that I'm getting something like the output
> of rnorm() by feeding it an empty list is just serendipity. But
> it would seem that there may be something subtle going on here.
> Any ideas?

Brian D. Ripley,        
Professor of Applied Statistics,
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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