Convergence failure in time trend estimation with ARIMA

[Alex Mai]

Dear statalist,

I am applying -arima- to a simple log-linear time trend equation ln(y)=a+bt+u (the differenced form is dln(y)=b+u). It is a very short time series database with only 22 observations. However, I face a convergence problem. The following shows the last part of the outcome returned by stata.

May I ask what are the possible reasons for such convergence failure and how to solve it?

Thank you very much.

Iteration 195: log likelihood =  6.8891918  (not concave)
Iteration 196: log likelihood =  6.8891918  (not concave)
Iteration 197: log likelihood =  6.8891918  (not concave)
Iteration 198: log likelihood =  6.8891918  (not concave)
Iteration 199: log likelihood =  6.8891918  (not concave)
(switching optimization to BFGS)
BFGS stepping has contracted, resetting BFGS Hessian (92)
Iteration 200: log likelihood =  6.8891918  
BFGS stepping has contracted, resetting BFGS Hessian (93)
Iteration 201: log likelihood =  6.8891918  (backed up)
BFGS stepping has contracted, resetting BFGS Hessian (94)
Iteration 202: log likelihood =  6.8891918  (backed up)
BFGS stepping has contracted, resetting BFGS Hessian (95)
Iteration 203: log likelihood =  6.8891918  (backed up)
BFGS stepping has contracted, resetting BFGS Hessian (96)
Iteration 204: log likelihood =  6.8891918  (backed up)
BFGS stepping has contracted, resetting BFGS Hessian (97)
Iteration 205: log likelihood =  6.8891918  (backed up)
BFGS stepping has contracted, resetting BFGS Hessian (98)
Iteration 206: log likelihood =  6.8891918  (backed up)
BFGS stepping has contracted, resetting BFGS Hessian (99)
Iteration 207: log likelihood =  6.8891918  (backed up)
flat log likelihood encountered, cannot find uphill direction
r(430);

end of do-file

[Alex Mai]

Any suggestions would be appreciated! Thank you!

[Phil Bromiley]

You'll increase your chances of a useful answer by following to FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

I'm afraid I don't use arima. The normal suggestion to a convergence problem is to mess with the maximization (allow for different stepping rules, use the difficult option, try starting values), or start with a very simple model and then build up. However, it would not surprise me if you found much of your problem stems from a very small data set.

[Alex Mai]

You'll increase your chances of a useful answer by following to FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

I'm afraid I don't use arima. The normal suggestion to a convergence problem is to mess with the maximization (allow for different stepping rules, use the difficult option, try starting values), or start with a very simple model and then build up. However, it would not surprise me if you found much of your problem stems from a very small data set.

Dear Phil,

Thank you very much. Your last sentence seems to imply that convergence problem is likely to stem from small sample size (sorry, but I am not quite sure if I interpret your point correctly), so may I ask the reasoning underlying this point?

[Alex Mai]

Any additional suggestions would be appreciated. May I ask why small sample size is more likely to generate convergence failure? Thank you!

[Alex Mai]

You'll increase your chances of a useful answer by following to FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

I'm afraid I don't use arima. The normal suggestion to a convergence problem is to mess with the maximization (allow for different stepping rules, use the difficult option, try starting values), or start with a very simple model and then build up. However, it would not surprise me if you found much of your problem stems from a very small data set.

Dear Phil,

Sorry for bothering you again. But may I ask a question on the relationship between small sample size and convergence failure?
Your early reply to my question seems to imply that small sample size is likely to generate convergence problem (if I interpret your point correctly).
So can I ask about the underlying reason for small sample size to generate convergence failure?

Thank you very much!

[Alex Mai]

Any suggestions would be appreciated! Many thanks!