Re: arima0() (PR#314)

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Subject: Re: arima0() (PR#314)
From: Prof Brian D Ripley (
Date: Tue 09 Nov 1999 - 18:11:17 EST

Message-ID: <Pine.GSO.4.05.9911090759220.26939-100000@auk.stats>

On Sun, 7 Nov 1999 wrote:

> Full_Name: Ahmad Abu Hammour
> Version: rw0651
> OS: windows 95
> Submission from: (NULL) (
> Although I know that "ts package" is preliminary, I wanted to compare the
> results from R and SPSS. I ran ARIMA(2,1,2) in both softwares. I got NaN in
> standard errors of coefficients from R and real figures from SPSS. I changed
> "delta" in R to match that used by SPSS, I received results with no NaNs but
> different from those from SPSS specially in MA coefficients. They came out
> negative numbers while positive from SPSS.

Mr Hammour sent me the data privately. Running

arima0(y0, order=c(2,1,2), delta=-1)

I get

arima0(x = y0, order = c(2, 1, 2), delta = -1)

    ar1 ar2 ma1 ma2
-0.7686 0.1519 -0.1143 -0.8857

Approx standard errors:
   ar1 ar2 ma1 ma2
0.1917 0.0912 0.1765 0.1762

sigma^2 estimated as 109859: log likelihood = -890.65, aic = 1789.3

[Using the default delta of 0.01 in this case gives inaccurate results:
but it is a very badly determined model.]

SPSS had

Number of residuals 123
Standard error 337.30778
Log likelihood -890.6952
AIC 1789.3904
SBC 1800.6391

           Variables in the Model:

                B SEB T-RATIO APPROX. PROB.

AR1 -.78319350 .16013797 -4.8907421 .00000318
AR2 .16191191 .09435030 1.7160719 .08875107
MA1 .07993592 .54769107 .1459508 .88420721
MA2 .91762463 .49337224 1.8599032 .06536851

>Warning # 16567. Command name: ARIMA
>Our tests have determined that the estimated model lies close to the
>boundary of the invertibility region. Although the moving average
>parameters are probably correctly estimated, their standard errors and
>covariances should be considered suspect.

So (up to the MA sign change, a matter of definition) the estimates
differ by 1 se or so. However, SPSS has given a warning, and the
log-likelihoods are similar but R's is larger. This suggests that

- There is no practical difference between the results, and

- R's optimizer has done a better job.

- R works on transformed scale and so has more chance of getting se's
  close to the boundary (but the error distribution will be very far from

- This is not a good model for the data.

If there is a bug at all here, it would appear to be in SPSS.

Moral: take warnings seriously.

Brian D. Ripley,        
Professor of Applied Statistics,
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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