[R-sig-Finance] garchFit and NAs

[Spencer Graves]

	  You don't provide a simple, self-contained example, so I can't be 
certain of what you are seeing.  However, I tried a "garchFit" example 
in "~/fSeries/demo/xmpDWChapter34.R", as suggested in the "garchFit" 
help file, and it seemed to return sensible answers.  Then I modified it 
with "formula.mean = ~arma(0, 2)" and 'cond.dist="dsged"' as in your 
example.  That completed in just under 13 minutes, if my memory is 
correct.  When I tried the same example without the 'cond.dist="dsged"', 
it seemed to run forever without making progress.  Over an hour later, I 
had such trouble killing it that I would up rebooting!

	  Since the example that ran took almost 13 minutes, I'm not eager to 
rerun it.  However, as I recall, the example from xmpDWChapter34.R 
didn't have the problem you identified, but the "~arma(0, 2)" 
modification did.  To explore this further, I used "str" to see the 
structure of the garchFit output.  In that, I found something called 
"hessian".  If I'm not mistaken, I believe the square roots of the 
diagonals of the inverse of "hessian" should be the approximate standard 
errors;  if not, the difference should be something like a factor of the 
standard deviation of the residuals.  You can check this for an example 
that works.  For the "~arma(0, 2)" modification, I computed the 
eigenvalues of the "hessian", and found that it was NOT positive 
definite, as it should be:  Instead it had some positive and some 
negative eigenvalues.  I'm guessing that this means that the formally 
computed approximate covariance matrix might have negative numbers on 
its diagonal.  If so, this would correspond to imaginary standard errors 
and would generate the NAs you reported.

	  I'm not completely certain how to interpret this in the context of 
your application, but I'm guessing that the algorithm is getting stuck 
in a saddle-point and is not actually maximizing the likelihood.  If you 
wanted to pursue this further, you could list the "garchFit" function to 
see what it does.  It might help to walk through it line-by-line, e.g., 
using "debug" (see, e.g., 
"http://finzi.psych.upenn.edu/R/Rhelp02a/archive/68215.html").  This 
will likely consist of a call to an optimizer.  You could find that, 
then experiment with evaluating the objective function over a moderately 
course grid, using e.g., expand.grid to generate a set of points at 
which to evaluate the grid, then evaluating the objective function at 
each such point in a loop, then studying the results, e.g., using 
'lattice' graphics.

	  I realize this won't solve your problem, but I think you are working 
in an area that has not yet been extensively studied.  Nevertheless, I 
hope this helps.

	  Spencer Graves

anass.mouhsine at sgcib.com wrote:
> Hi everybody,
> 
> When trying to fit an ARMA(0,2)-APARCH(1,1) model to a timeseries, it
> results in the following warning message:
> 
> NaNs produced in: sqrt(diag(fit$cvar))
> 
> the print function gives the following result
> 
> _______________________________________________________________________
> Title:
>  GARCH Modelling
> 
> Call:
>  garchFit(formula.mean = ~arma(0, 2), formula.var = ~aparch(1,
>     1), series = seriemul, cond.dist = "dsged")
> 
> Mean and Variance Equation:
>  ~arma(0, 2) + ~aparch(1, 1)
> 
> Conditional Distribution:
>  dsged
> 
> Coefficient(s):
>        mu        ma1        ma2      omega     alpha1     gamma1
> -0.478628   0.356290   0.054928   1.472516   0.944778   0.418131
>     beta1      delta       skew      shape
>  0.306527   1.912457   0.541992   1.304578
> 
> Error Analysis:
>         Estimate  Std. Error  t value Pr(>|t|)
> mu     -0.478628    0.066091   -7.242 4.42e-13 ***
> ma1     0.356290    0.096042    3.710 0.000207 ***
> ma2     0.054928    0.055839    0.984 0.325272
> omega   1.472516    0.223275    6.595 4.25e-11 ***
> alpha1  0.944778    0.213975    4.415 1.01e-05 ***
> gamma1  0.418131    0.094418    4.428 9.49e-06 ***
> beta1   0.306527          NA       NA       NA
> delta   1.912457          NA       NA       NA
> skew    0.541992    0.004978  108.879  < 2e-16 ***
> shape   1.304578          NA       NA       NA
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> Log Likelihood:
>  764.6944    normalized:  2.044638
> _______________________________________________________________________
> 
> My question is:
> --> How are these NaNs produced?
> --> How can we read and interpret the NAs in the result?
> 
> Thank you in advance for your help,
> 
> Anass
> 
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