In a spatial model for extreme wind speeds (2 sec gust) we get shape parameters between -0.9 and -1.5. Although achieved return values are very reasonable, the magnitude of the shape parameter seems weird. Rather than maximum likelihood, the parameter is modeled with respect to the Cramer von Mises criterion. So the usual constraint for shape less than -1 that make maximum likelihood estimators unlikely to be obtained does not apply. Can anybody comment on such low shape parameters? Is there a (funded) argumentation for accepting or refusing such values?
Hi Paul,
thanks for your answer, I will check the fit anyway. The "problem" ist the fact, that local estimations (using maximum likelihood) of the data series give shape parameters mostly between 0 and -0.6, while the spatial model shows those very negative values less than -0.9. We could speculate, that the estimation of the shape parameter for the quite short data series used (approx. 20 years) leads to unreliable values, and the spatial model stabilizes them. Would you agree with that?
Paul you once told me the GEV shape parameter is expected to be between -0.5 to 0.5 in practice, otherwise we end up with a problem of infinite variance. Are we having an exceptional case here? Or is it because the data is not sufficient as stated?
Dear Harald,
I would be curious about two things:
- have you used the entire year to calculate your estimates? It seems to me that the quality of the estimate can be very poor if one ignores the seasonal non-stationarity.
- Are you using yearly maxima? have you tried taking the max over 2 years at a time to see if the shape parameter remains the same? Of course, I realize you would have only 10 blocks of data, but it would be interesting to know.
Best regards,
Sophie.
Dear Sophie, nice to hear from you :-)
Yes we used the entire year. Do you mean to take seasonal, rather than yearly maxima? I can try with 2-yearly maxima. That could perhaps smooth the data somewhat, which is "easier" to model. What do you expect?
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