Hurricanes and errors of reasoning?

One of the topics discussed related to the "medium term" view of hurricane risk.  The crux of this debate is whether hurricane activity is elevated above long term average rates for some reason.

The reason might be climate change, natural cycles or (as I suspect) a bit of both.

AIR provides two hurricane event catalogues, to quote from their presentation at the meeting:

– "The Standard Catalog is a long-term view of risk conditioned on the characteristics of all Atlantic hurricane seasons since 1900"

– "The Warm SST (WSST) Catalog is also a long-term view of risk, but conditioned on only those seasons since 1900 in which the Atlantic Ocean has been warmer than average (observed ~50% of the time)"

They also, quite correctly (and usefully) point out "Neither of the stochastic catalogs was designed to “forecast” losses" a subject that our forthcoming emerging risks paper on forecasting and insurance will discuss in more detail.

Their presentation then makes an error of reasoning as far I can see (though I don’t know what they said verbally and powerpoint slides can be misleading).  They say...

"Both views of risk are credible and scientifically valid, though the WSST catalog is based on less data, and is thus subject to elevated levels of uncertainty"

Firstly, the "uncertainty" they are speaking of (I believe) is the uncertainty in the distribution of hurricane losses in their catalogue - this would include the average loss.  Their model provides an estimate of the average loss and they argue that this estimate is more uncertain when the WSST catalogue is used because it has less data.

But, this is only true if the underlying process is, to use a technical term, stationary.  A stationary process is one which has a constant (unknown) underlying mean.  It’s obvious that the more observations you make of a stationary process, the more you learn about it.

If the underlying process is not stationary, say it has a cycle, or a upwards trend - then a long term average will be highly uncertain.  At almost all points in the cycle it will be a biased (i.e. not very good) estimator.

If sea surface temperature is a good predictor of mean hurricane activity then conditioning on this variable would give a better - and more certain estimator.

At Lloyd's we've made it clear in our ICA guidance that we believe the hurricane time series is not stationary:

"Models are based on past experience and it is likely that over time this experience will become out of date due to all manner of trends.... there is strong evidence that hurricane risk in the North Atlantic is raised above long term averages.... "

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