arima0() (PR#314)

[Prof Brian D Ripley]

On Sun, 7 Nov 1999 hammour@msn.com wrote:

> Full_Name: Ahmad Abu Hammour
> Version: rw0651
> OS: windows 95
> Submission from: (NULL) (63.23.128.44)
> 
> 
> 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

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

Coefficients:
    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
  normal).

- 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,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
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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