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Extreme Value Analysis (extreme + value_analysis)
Selected AbstractsExtreme value analysis in biometricsBIOMETRICAL JOURNAL, Issue 2 2009Jürg Hüsler Abstract We review some approaches of extreme value analysis in the context of biometrical applications. The classical extreme value analysis is based on iid random variables. Two different general methods are applied, which will be discussed together with biometrical examples. Different estimation, testing, goodness-of-fit procedures for applications are discussed. Furthermore, some non-classical situations are considered where the data are possibly dependent, where a non-stationary behavior is observed in the data or where the observations are not univariate. A few open problems are also stated. [source] Extreme US stock market fluctuations in the wake of 9/11JOURNAL OF APPLIED ECONOMETRICS, Issue 1 2008S. T. M. Straetmans We apply extreme value analysis to US sectoral stock indices in order to assess whether tail risk measures like value-at-risk and extremal linkages were significantly altered by 9/11. We test whether semi-parametric quantile estimates of ,downside risk' and ,upward potential' have increased after 9/11. The same methodology allows one to estimate probabilities of joint booms and busts for pairs of sectoral indices or for a sectoral index and a market portfolio. The latter probabilities measure the sectoral response to macro shocks during periods of financial stress (so-called ,tail-,s'). Taking 9/11 as the sample midpoint we find that tail-,s often increase in a statistically and economically significant way. This might be due to perceived risk of new terrorist attacks. Copyright © 2008 John Wiley & Sons, Ltd. [source] A new class of models for bivariate joint tailsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 1 2009Alexandra Ramos Summary., A fundamental issue in applied multivariate extreme value analysis is modelling dependence within joint tail regions. The primary focus of this work is to extend the classical pseudopolar treatment of multivariate extremes to develop an asymptotically motivated representation of extremal dependence that also encompasses asymptotic independence. Starting with the usual mild bivariate regular variation assumptions that underpin the coefficient of tail dependence as a measure of extremal dependence, our main result is a characterization of the limiting structure of the joint survivor function in terms of an essentially arbitrary non-negative measure that must satisfy some mild constraints. We then construct parametric models from this new class and study in detail one example that accommodates asymptotic dependence, asymptotic independence and asymmetry within a straightforward parsimonious parameterization. We provide a fast simulation algorithm for this example and detail likelihood-based inference including tests for asymptotic dependence and symmetry which are useful for submodel selection. We illustrate this model by application to both simulated and real data. In contrast with the classical multivariate extreme value approach, which concentrates on the limiting distribution of normalized componentwise maxima, our framework focuses directly on the structure of the limiting joint survivor function and provides significant extensions of both the theoretical and the practical tools that are available for joint tail modelling. [source] Anticipating catastrophes through extreme value modellingJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 4 2003Stuart Coles Summary. When catastrophes strike it is easy to be wise after the event. It is also often argued that such catastrophic events are unforeseeable, or at least so implausible as to be negligible for planning purposes. We consider these issues in the context of daily rainfall measurements recorded in Venezuela. Before 1999 simple extreme value techniques were used to assess likely future levels of extreme rainfall, and these gave no particular cause for concern. In December 1999 a daily precipitation event of more than 410 mm, almost three times the magnitude of the previously recorded maximum, caused devastation and an estimated 30000 deaths. We look carefully at the previous history of the process and offer an extreme value analysis of the data,with some methodological novelty,that suggests that the 1999 event was much more plausible than the previous analyses had claimed. Deriving design parameters from the results of such an analysis may have had some mitigating effects on the consequences of the subsequent disaster. The themes of the new analysis are simple: the full exploitation of available data, proper accounting of uncertainty, careful interpretation of asymptotic limit laws and allowance for non-stationarity. The effect on the Venezuelan data analysis is dramatic. The broader implications are equally dramatic; that a naïve use of extreme value techniques is likely to lead to a false sense of security that might have devastating consequences in practice. [source] Simulation and extremal analysis of hurricane eventsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 3 2000E. Casson In regions affected by tropical storms the damage caused by hurricane winds can be catastrophic. Consequently, accurate estimates of hurricane activity in such regions are vital. Unfortunately, the severity of events means that wind speed data are scarce and unreliable, even by standards which are usual for extreme value analysis. In contrast, records of atmospheric pressures are more complete. This suggests a two-stage approach: the development of a model describing spatiotemporal patterns of wind field behaviour for hurricane events; then the simulation of such events, using meteorological climate models, to obtain a realization of associated wind speeds whose extremal characteristics are summarized. This is not a new idea, but we apply careful statistical modelling for each aspect of the model development and simulation, taking the Gulf and Atlantic coastlines of the USA as our study area. Moreover, we address for the first time the issue of spatial dependence in extremes of hurricane events, which we find to have substantial implications for regional risk assessments. [source] The multivariate Gaussian tail model: an application to oceanographic dataJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 1 2000P. Bortot Optimal design of sea-walls requires the extreme value analysis of a variety of oceanographic data. Asymptotic arguments suggest the use of multivariate extreme value models, but empirical studies based on data from several UK locations have revealed an inadequacy of this class for modelling the types of dependence that are often encountered in such data. This paper develops a specific model based on the marginal transformation of the tail of a multivariate Gaussian distribution and examines its utility in overcoming the limitations that are encountered with the current methodology. Diagnostics for the model are developed and the robustness of the model is demonstrated through a simulation study. Our analysis focuses on extreme sea-levels at Newlyn, a port in south-west England, for which previous studies had given conflicting estimates of the probability of flooding. The novel diagnostics suggest that this discrepancy may be due to the weak dependence at extreme levels between wave periods and both wave heights and still water levels. The multivariate Gaussian tail model is shown to resolve the conflict and to offer a convincing description of the extremal sea-state process at Newlyn. [source] Time variation in the tail behavior of Bund future returnsTHE JOURNAL OF FUTURES MARKETS, Issue 4 2004Thomas Werner The literature on the tail behavior of asset prices focuses mainly on the foreign exchange and stock markets, with only a few articles dealing with bonds or bond futures. The present article addresses this omission. It focuses on three questions using extreme value analysis: (a) Does the distribution of Bund future returns have heavy tails? (b) Do the tails change over time? (c) Does the tail index provide information that is not captured by a standard VaR approach? The results are as follows: (a) The distribution of high-frequency returns of the Bund future is indeed characterized by heavy tails. The tails are thinner for lower frequencies, but remain significantly heavy even for daily data. (b) There are statistically significant breaks in the tails of the return distribution. (c) The likelihood of extreme price movements suggested by extreme value theory differs from that obtained by standard risk measures. This suggests that the tail index does indeed provide information not contained in volatility measures. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:387,398, 2004 [source] Extreme value analysis in biometricsBIOMETRICAL JOURNAL, Issue 2 2009Jürg Hüsler Abstract We review some approaches of extreme value analysis in the context of biometrical applications. The classical extreme value analysis is based on iid random variables. Two different general methods are applied, which will be discussed together with biometrical examples. Different estimation, testing, goodness-of-fit procedures for applications are discussed. Furthermore, some non-classical situations are considered where the data are possibly dependent, where a non-stationary behavior is observed in the data or where the observations are not univariate. A few open problems are also stated. [source] | |||||||||||||