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| Titel |
When black swans come in bunches: modelling the impact of temporal correlations on the return periods of heavy tailed risk |
| VerfasserIn |
Nicholas Watkins, Sam Rosenberg, Sandra Chapman, Mark Naylor, Mervyn Freeman |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250056665
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| Zusammenfassung |
| For any natural hazard, the question of when the next “extreme event” (or “black swan”) is
expected is of obvious importance. We here consider natural hazards defined in a
very broad sense, as fluctuations in natural time series with the potential to pose a
significant human or economic threat. In the environmental sciences users often
frame such questions in terms of average “return periods”, e.g. “is an X meter rise
in the Thames water level a 1-in-Y year event ?”. Frequently, however, we also
care about the emergence of correlation, and whether the probability of several
big events coming in close succession is truly independent, i.e. “bunched black
swans”. We can thus see that a “big event”, or a “burst”, seen from the point of
view of its integrated damage and loss, might be a single, very large, event, or,
instead, could in fact be a correlated series of “smaller (i.e. less wildly fluctuating)
events.
Several stochastic approaches exist that provide quantitative information about bursts.
Some are more focused on the probability of single large events; others are more
concerned with extended dwell times above a given spatiotemporal threshold: Extreme
Value Theory (EVT); the theory of records; level sets; sojourn times; and models of
“avalanches” in the non-Brownian space-time activity of non-equilibrium systems .
However, the state of the art is not yet adequate for several reasons. Firstly, the
above-mentioned approaches differ in fundamental aspects. The first group, EVT, is
perhaps the best known of the above methods to geoscientists; it is used to derive and
quantify, for example, the probability of exceedance for the failure of a dam. It is
concerned with the distribution obeyed by the extremes of datasets, e.g. the 100
values obtained by considering the largest daily temperature recorded in each of the
years of a century. However, the fundamental theorems on which EVT is built are
based on independent identically distributed data and so take no account of memory
and correlation that characterise many natural hazard time series; ignoring this
fundamentally limits our ability to forecast. A second group of approaches, by contrast,
explicitly has notions of time and thus possible nonstationarity built in. In record
breaking statistics, a record is defined in the sense used in everyday language, to be the
largest value yet recorded in a time series, for example, the Sumatran boxing day
earthquake is the largest earthquake to be digitally recorded. The third group of
approaches (e.g. avalanches) are explicitly spatiotemporal and so include spatial
structure.
In practice which methods are adopted has also differed between, and within, application
domains, sometimes reflecting data limitations. Although knowledge is understandably not
yet integrated, nonetheless significant efforts have started along this direction. I will discuss
an example of such unifying efforts & will show preliminary results [Watkins et
al, PRE, 2009] ssing a standard model, linear fractional stable motion (LFSM),
that explicitly includes both heavy tails and long range dependence, to study how
these two effects contribute to the probability of large bursts in stochastic time
series. |
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