197 research outputs found
Convergence to extremal processes in random environments and extremal ageing in SK models
This paper extends recent results on aging in mean field spin glasses on
short time scales, obtained by Ben Arous and Gun [2] in law with respect to the
environment, to results that hold almost surely, respectively in probability,
with respect to the environment. It is based on the methods put forward in
Gayrard [8,9] and naturally complements Bovier and Gayrard [6].Comment: Revised version contains minor change
Extreme Value Theory versus traditional GARCH approaches applied to financial data: a comparative evaluation
Although stock prices fluctuate, the variations are relatively small and are frequently assumed to be normally distributed on a large time scale. But sometimes these fluctuations can become determinant, especially when unforeseen large drops in asset prices are observed that could result in huge losses or even in market crashes. The evidence shows that these events happen far more often than would be expected under the generalised assumption of normally distributed financial returns. Thus it is crucial to model distribution tails properly so as to be able to predict the frequency and magnitude of extreme stock price returns. In this paper we follow the approach suggested by McNeil and Frey in 2000 and combine GARCH-type models with the extreme value theory to estimate the tails of three financial index returns Âż S&P 500, FTSE 100 and NIKKEI 225 Âż representing three important financial areas in the world. Our results indicate that EVT-based conditional quantile estimates are more accurate than those from conventional GARCH models assuming normal or StudentÂżs t distribution innovations when doing not only in-sample but also out-of-sample estimation. Moreover, these results are robust to alternative GARCH model specifications. The findings of this paper should be useful to investors in general, since their goal is to be able to forecast unforeseen price movements and take advantage of them by positioning themselves in the market according to these predictions
Statistical modeling of ground motion relations for seismic hazard analysis
We introduce a new approach for ground motion relations (GMR) in the
probabilistic seismic hazard analysis (PSHA), being influenced by the extreme
value theory of mathematical statistics. Therein, we understand a GMR as a
random function. We derive mathematically the principle of area-equivalence;
wherein two alternative GMRs have an equivalent influence on the hazard if
these GMRs have equivalent area functions. This includes local biases. An
interpretation of the difference between these GMRs (an actual and a modeled
one) as a random component leads to a general overestimation of residual
variance and hazard. Beside this, we discuss important aspects of classical
approaches and discover discrepancies with the state of the art of stochastics
and statistics (model selection and significance, test of distribution
assumptions, extreme value statistics). We criticize especially the assumption
of logarithmic normally distributed residuals of maxima like the peak ground
acceleration (PGA). The natural distribution of its individual random component
(equivalent to exp(epsilon_0) of Joyner and Boore 1993) is the generalized
extreme value. We show by numerical researches that the actual distribution can
be hidden and a wrong distribution assumption can influence the PSHA negatively
as the negligence of area equivalence does. Finally, we suggest an estimation
concept for GMRs of PSHA with a regression-free variance estimation of the
individual random component. We demonstrate the advantages of event-specific
GMRs by analyzing data sets from the PEER strong motion database and estimate
event-specific GMRs. Therein, the majority of the best models base on an
anisotropic point source approach. The residual variance of logarithmized PGA
is significantly smaller than in previous models. We validate the estimations
for the event with the largest sample by empirical area functions. etc
Observation of Coherent Elastic Neutrino-Nucleus Scattering
The coherent elastic scattering of neutrinos off nuclei has eluded detection
for four decades, even though its predicted cross-section is the largest by far
of all low-energy neutrino couplings. This mode of interaction provides new
opportunities to study neutrino properties, and leads to a miniaturization of
detector size, with potential technological applications. We observe this
process at a 6.7-sigma confidence level, using a low-background, 14.6-kg
CsI[Na] scintillator exposed to the neutrino emissions from the Spallation
Neutron Source (SNS) at Oak Ridge National Laboratory. Characteristic
signatures in energy and time, predicted by the Standard Model for this
process, are observed in high signal-to-background conditions. Improved
constraints on non-standard neutrino interactions with quarks are derived from
this initial dataset
Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management
Recent literature has trumpeted the claim that extreme value theory (EVT) holds promise for accurate estimation of extreme quantiles and tail probabilities of financial asset returns, and hence hold promise for advances in the management of extreme financial risks. Our view, based on a disinterested assessment of EVT from the vantage point of financial risk management, is that the recent optimism is partly appropriate but also partly exaggerated, and that at any rate much of the potential of EVT remains latent. We substantiate this claim by sketching a number of pitfalls associate with use of EVT techniques. More constructively, we show how certain of the pitfalls can be avoided, and we sketch a number of explicit research directions that will help the potential of EVT to be realized
On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model
We consider the coupling from the past implementation of the random-cluster
heat-bath process, and study its random running time, or coupling time. We
focus on hypercubic lattices embedded on tori, in dimensions one to three, with
cluster fugacity at least one. We make a number of conjectures regarding the
asymptotic behaviour of the coupling time, motivated by rigorous results in one
dimension and Monte Carlo simulations in dimensions two and three. Amongst our
findings, we observe that, for generic parameter values, the distribution of
the appropriately standardized coupling time converges to a Gumbel
distribution, and that the standard deviation of the coupling time is
asymptotic to an explicit universal constant multiple of the relaxation time.
Perhaps surprisingly, we observe these results to hold both off criticality,
where the coupling time closely mimics the coupon collector's problem, and also
at the critical point, provided the cluster fugacity is below the value at
which the transition becomes discontinuous. Finally, we consider analogous
questions for the single-spin Ising heat-bath process
- …