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Because of its potential to "predict the unpredictable," Extreme Value Theory (EVT) and its methodology are currently in the spotlight. EVT affords some insight into extreme tails and maxima where standard models have proved unreliable. This is achieved with semi-parametric models which only specify the distributional shapes of maxima or of extreme tails. The rationale for these models are very basic limit and stability arguments.
Bringing together world-recognized authorities, Extreme Values in Finance, Telecommunications, and the Environment puts to rest some of the myths and misconceptions of EVT. It explores the application, use, and theory of extreme values in the areas of finance, insurance, the environment, and telecommunications. The book reviews the way in which this paradigm can answer questions in climatology, insurance, and finance, covers parts of univariate extreme values theory, and discusses estimation, diagnostics, and multivariate extremes. It presents issues in data network modeling and examines aspects of Value-at-Risk (VaR) and its estimation based on EVT. The final chapter gives an overview of multivariate extreme value distributions and the problem of measuring extremal dependencies.
Considered one of the hottest ideas in risk management, EVT is designed to allow anyone faced with calculating risky situations to determine the chances of being hit with one or even multiple catastrophic events. It provides a statistical methodology for dealing with the prediction of events which are so rare that they appear impossible. Presenting information from the forefront of knowledge and research, Extreme Values in Finance, Telecommunications, and the Environment brings you up to speed on current issues and techniques in EVT.
Statistical Methods for Spatio-Temporal Systems presents current
statistical research issues on spatio-temporal data modeling and
will promote advances in research and a greater understanding
between the mechanistic and the statistical modeling communities.
Contributed by leading researchers in the field, each
self-contained chapter starts with an introduction of the topic and
progresses to recent research results. Presenting specific examples
of epidemic data of bovine tuberculosis, gastroenteric disease, and
the U.K. foot-and-mouth outbreak, the first chapter uses stochastic
models, such as point process models, to provide the probabilistic
backbone that facilitates statistical inference from data. The next
chapter discusses the critical issue of modeling random growth
objects in diverse biological systems, such as bacteria colonies,
tumors, and plant populations. The subsequent chapter examines data
transformation tools using examples from ecology and air quality
data, followed by a chapter on space-time covariance functions. The
contributors then describe stochastic and statistical models that
are used to generate simulated rainfall sequences for hydrological
use, such as flood risk assessment. The final chapter explores
Gaussian Markov random field specifications and Bayesian
computational inference via Gibbs sampling and Markov chain Monte
Carlo, illustrating the methods with a variety of data examples,
such as temperature surfaces, dioxin concentrations, ozone
concentrations, and a well-established deterministic dynamical
weather model.
Statistical Methods for Spatio-Temporal Systems presents current
statistical research issues on spatio-temporal data modeling and
will promote advances in research and a greater understanding
between the mechanistic and the statistical modeling communities.
Contributed by leading researchers in the field, each
self-contained chapter starts with an introduction of the topic and
progresses to recent research results. Presenting specific examples
of epidemic data of bovine tuberculosis, gastroenteric disease, and
the U.K. foot-and-mouth outbreak, the first chapter uses stochastic
models, such as point process models, to provide the probabilistic
backbone that facilitates statistical inference from data. The next
chapter discusses the critical issue of modeling random growth
objects in diverse biological systems, such as bacteria colonies,
tumors, and plant populations. The subsequent chapter examines data
transformation tools using examples from ecology and air quality
data, followed by a chapter on space-time covariance functions. The
contributors then describe stochastic and statistical models that
are used to generate simulated rainfall sequences for hydrological
use, such as flood risk assessment. The final chapter explores
Gaussian Markov random field specifications and Bayesian
computational inference via Gibbs sampling and Markov chain Monte
Carlo, illustrating the methods with a variety of data examples,
such as temperature surfaces, dioxin concentrations, ozone
concentrations, and a well-established deterministic dynamical
weather model.
1. 1 Introduction In economics, one often observes time series that
exhibit different patterns of qualitative behavior, both regular
and irregular, symmetric and asymmetric. There exist two different
perspectives to explain this kind of behavior within the framework
of a dynamical model. The traditional belief is that the time
evolution of the series can be explained by a linear dynamic model
that is exogenously disturbed by a stochastic process. In that
case, the observed irregular behavior is explained by the influence
of external random shocks which do not necessarily have an economic
reason. A more recent theory has evolved in economics that
attributes the patterns of change in economic time series to an
underlying nonlinear structure, which means that fluctua tions can
as well be caused endogenously by the influence of market forces,
preference relations, or technological progress. One of the main
reasons why nonlinear dynamic models are so interesting to
economists is that they are able to produce a great variety of
possible dynamic outcomes - from regular predictable behavior to
the most complex irregular behavior - rich enough to meet the
economists' objectives of modeling. The traditional linear models
can only capture a limited number of possi ble dynamic phenomena,
which are basically convergence to an equilibrium point, steady
oscillations, and unbounded divergence. In any case, for a lin ear
system one can write down exactly the solutions to a set of
differential or difference equations and classify them."
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