[Rd] Fix for bug in arima function

[peter dalgaard]

On 21 May 2015, at 10:35 , Martin Maechler <maechler at lynne.stat.math.ethz.ch> wrote:

>> 
>> I noticed that the 3.2.1 release cycle is about to start.  Is there any
>> chance that this fix will make it into the next version of R?
>> 
>> This bug is fairly serious: getting the wrong variance estimate leads to
>> the wrong log-likelihood and the wrong AIC, BIC etc, which can and does
>> lead to suboptimal model selection.  If it's not fixed, this issue will
>> affect every student taking our time series course in Fall 2015 (and
>> probably lots of other students in other time series courses).  When I
>> taught time series in Spring 2015, I had to teach students how to work
>> around the bug, which wasted class time and shook student confidence in R.
>> It'd be great if we didn’t have to deal with this issue next semester.
>> 
>> Again, the fix is trivial:
>> 
>> --- a/src/library/stats/R/arima.R
>> +++ b/src/library/stats/R/arima.R
>> @@ -211,8 +211,10 @@ arima <- function(x, order = c(0L, 0L, 0L),
>>         if(fit$rank == 0L) {
>>             ## Degenerate model. Proceed anyway so as not to break old code
>>             fit <- lm(x ~ xreg - 1, na.action = na.omit)
>> +            n.used <- sum(!is.na(resid(fit))) - length(Delta)
>> +        } else {
>> +            n.used <- sum(!is.na(resid(fit)))
>>         }
>> -        n.used <- sum(!is.na(resid(fit))) - length(Delta)
>>         init0 <- c(init0, coef(fit))
>>         ses <- summary(fit)$coefficients[, 2L]
>>         parscale <- c(parscale, 10 * ses)
>> 
> 
> Yes, such a change *is* small in the source code.
> But we have to be sure about  its desirability.
> 
> In another post about this you mention "REML", and I think we
> really are discussing if variance estimates should use a
> denominator of  'n'  or 'n - p' in this case.
> 
> 
>> The patch that introduced the bug (
>> https://github.com/wch/r-source/commit/32f633885a903bc422537dc426644f743cc645e0
>> ) was designed to change the initialization for the optimization routine.
> 
>> The proposed fix leaves the deliberate part of the patch unchanged (it
>> preserves the value of "init0").
> 
> I can confirm this... a change introduced in R 3.0.2.
> 
> I'm about to commit changes ... after also adding a proper
> regression test.
> 

Be careful here! I was just about to say that the diagnosis is dubious, and that the patch could very well be wrong!!

AFAICT, the issue is that n.used got changed from being based on lm(x~...) to lm(dx~...) where dx is the differenced series. Now that surely loses one observation in arima(.,1,.), most likely unintentionally, but it is not at all clear that the fix is not to subtract length(Delta) -- that code has been there long before the changes in 3.0.2.

I'd expect that a safer fix would be to add back the orders of the the two differencing operations.

> Martin Maechler, ETH Zurich

-- 
Peter Dalgaard, Professor,
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