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Re: Problem with the Hannan Rissanen procedure

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  • Subject: [mg65620] Re: [mg65553] Problem with the Hannan Rissanen procedure
  • From: Darren Glosemeyer <darreng at>
  • Date: Tue, 11 Apr 2006 04:04:32 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

The Inverse message will get generated if an inverse is taken of a badly 
conditioned matrix, for instance, a matrix with very different row scales.

In[1]:= Inverse[{{1., 10.^-6}, {10.^-16, 10.^-10}}]

Inverse::luc: Result for Inverse of badly conditioned matrix
                -6         -16       -10
     {{1., 1. 10  }, {1. 10   , 1. 10   }} may contain significant 
numerical errors.

                                -6       10
Out[1]= {{1., -10000.}, {-1. 10  , 1. 10  }}

It is tough to say whether or not this should be cause for concern in your 
case without seeing an explicit example.

In a few examples I tried, the message was returned when the values of 
kmax, pmax, qmax were larger (around 5 for each in my case), but the 
message was not returned when these values were reduced.  This seemed to 
indicate to me that bad conditioning came about as a result of trying to 
fit the larger models, which in the end were not among the best models 
chosen for the data.  One possible check, assuming this is also the case 
for your examples, would be to re-run HannanRissanenEstimate with kmax, 
pmax, qmax reduced to match the largest values in the numModels chosen 
models.  If the message is no longer issued, the new results can be used 
without worrying about ill-conditioning.

Darren Glosemeyer
Wolfram Research

At 06:14 AM 4/7/2006 -0400, john.hawkin at wrote:
>I am doing time series research using mathematica, and I have come
>across the following problem.  When I run the command
>HannanRissanenEstimate[data, kmax, pmax, qmax, numModels]
>on certain sets of data, I get the error message:
>"Results for (op) of badly conditioned matrix (expr) may contain
>significant numerical errors"
>Where in this case op is "Inverse" and expr is my data.  In the help
>file it says the following about this error message:
>- Generated by a failure in the algorithm that is used in computing
>numerical solutions of linear systems of equations.
>- If you see this message in an example where it is not expected,
>please contact Technical Support.
>I don't believe there's any reason why the data I'm feeding in should
>be problematic.  Data that will generate this error include the
>following time series:
>AR models (AR(1), AR(2) and AR(3) generate it regularly, I have not
>tested others)
>The occasional ARMA model, very infrequently
>no MA models.
>All the AR models tested were stationary and all MA models were
>invertible, and all ARMA models were both.
>Does anyone know why this happens, if I should be concerned, and how I
>can fix it?
>-John Hawkin

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