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."