[R] optim() and ARIMA

Tue Jan 27 18:09:17 CET 2009

This is "surely" not a bug in "optim".  "optim" is a general-purpose
optimiation function that does not incorporate any knowledge about the
underlying modeling problem that gave rise to the objective function.
Therefore, the onus is on the modeler/user to ensure that the objective
function is well-behaved (i.e. it is correctly coded, properly scaled, any
potential singularities are properly handled, etc.).  As John Nash had
pointed out, it is always a good idea to properly scale the function such
that the components of gradient vector are similar, and to provide analytic
gradients.  Expecting a general-purpose optimizer to do the ground work for
you is not going to be fruitful.  

If you are not willing to do the groundwork then the next best thing is to
try different starting values.  Based on the knowledge of how ARIMA models
behave, you should be able to come up with multiple (sensible) starting
values.

Ravi.

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Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

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-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Gerard M. Keogh
Sent: Tuesday, January 27, 2009 11:17 AM
To: nashjc at uottawa.ca
Cc: r-help at r-project.org
Subject: Re: [R] optim() and ARIMA

Surely, this sounds like a bug in the optim function.

The rule of thumb with ts data is to scale so that data have mean 0 and unit
variance and then fit
   a) for non-seasonal data the IMA model (0,1,1); and
   b) for seasonal data so-called Airline Model (0,1,1)X(0,1,1)S see for
example A course in TS analysis by Daniel Pena.
These can usually be fit to most series unless they are very irregular (e.g.
mainly zeros) and then Box-Jenkins ARIMA is inappropriate.

The fit of any other model is then judged against these two models. If a
proposed model fit fails it is usual report the fault and then to step over
that model and try the next in sequence - optim should do this, if not then
it's a code fault.
Very often with nasty series only the 2 basic models can be fit and these
results are reported - but for these the parameters may not even fully
converge.
The moral of all this is that automatic modelling methods are handy but not
a substitute for looking at the acf and choosing an appropriate
parameterisation.

Can someone say whether optim has automatic outlier detection - this is a
must have with this type of procedure.

Gerard

             nashjc at uottawa.ca                                             
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             27/01/2009 15:45                                      Subject 
                                       Re: [R] optim() and ARIMA           

dhabby wrote:
    Last week I run in to a lot a problems triyng to fit an ARIMA model to a
    time series. The problem is that the internal process of the arima
function
    call function "optim" to estimate the model parameters, so far so
good...
    but my data presents a problem with the default method "BFGS" of the
optim
    function, the output error looks like this:

Error en optim(init[mask], armafn, method = "BFGS", hessian = TRUE, control
= optim.control,  :
  non-finite finite-difference value [7]

I don't know much about the calls from ARIMA to optim, but when I modified
Fletcher's 1970 VM method (called BFGS in R), I was aiming to make it
extremely robust to messy functions. (I had machinery with only 6 hex digits
for floating point and no guard digits. Furthermore, only 8K bytes for
program AND data. This was 1975/6.) However, BFGS needs gradients, and it is
clear there's some sort of trouble approximating them with finite
differences.

Changing optimization methods might succeed on this occasion, but your
problem is more likely bad scaling or some setup where your ARIMA model
essentially is not sensible. Can you duplicate the message on a small
example problem?

John Nash

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