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Bug in arima?

2 messages · Rick Bilonick, Brian Ripley

Rick Bilonick
# 
I'm using the fixed argument in arima. Shouldn't ar4, ar5, and ar6 
display as zero in the output?

Call:
arima(x = window(log(hhprice), start = c(1990, 1), end = c(2003, 3)), 
order = c(7,
    1, 0), xreg = window(ts.union(exa1 = lag(exa, -1), exa12 = lag(exa,
    -12), exb1 = lag(exb, -1), exc1 = lag(exc, -1), exc12 = lag(exc,
    -12)), start = c(1990, 1), end = c(2003, 3)), include.mean = FALSE, 
fixed = c(NA,
    NA, NA, 0, 0, 0, NA, NA, NA, NA, NA, NA))

Coefficients:
         ar1      ar2      ar3      ar4      ar5   ar6      ar7      
exa1      exa12      exb1      exc1      exc12
      0.0922  -0.1279  -0.2661  -0.0577  -0.0277  0.02  -0.2167   
-0.3015     0.3424    0.0281    0.0519     0.1715
s.e.  0.0789   0.0801   0.0742   0.0000   0.0000  0.00   0.0853    
0.0503     0.0515    0.0295    0.0257     0.0329

Also, is the documentation wrong?

 From ?arima:

fixed: optional numeric vector of the same length as the total
          number of parameters.  If supplied, only non-`NA' entries in
          `fixed' will be varied.  `transform.pars = TRUE' will be
          overridden if any AR parameters are fixed.

The non-NA entries in my fixed argument are zeroes. Aren't these "fixed" 
to zero so they don't vary when a call is made to optim? I thought that 
was the purpose of the argument. I only wan ar1, ar2, ar3, and ar7 in 
the model so I'm setting ar4, ar5, and ar6 to zero.

My main concern is that the predict.Arima function works correctly when 
using the fixed argument. I'm assuming, output display notwithstanding, 
that ar4-ar6 are actually fixed to zero when using fixed. When I try to 
manually make the forecast, the result is slightly different than what 
predict.Arima reports. I'm wondering if that is due to these 
coefficients not being set to zero?

Rick B.
Brian Ripley
# 
Here's a reproducible example (R 1.7.0)

set.seed(1)
x <- rnorm(100)
arima(x, order=c(7, 1, 0), fixed = c(NA, NA, NA, 0, 0, 0, NA),
      transform.pars = FALSE)

Coefficients:
          ar1      ar2      ar3  ar4  ar5  ar6     ar7
      -0.6838  -0.4126  -0.2236    0    0    0  0.0454
s.e.   0.0986   0.1115   0.0988    0    0    0  0.0843

and you did not set transform.pars.

Looks like the comment

   fixed: optional numeric vector of the same length as the total
          number of parameters.  If supplied, only non-`NA' entries in
          `fixed' will be varied.  `transform.pars = TRUE' will be
          overridden if any AR parameters are fixed.

has been copied from help(arima0) and is unimplemented in arima.
On Wed, 30 Apr 2003, Richard A. Bilonick wrote: