8,174 research outputs found
The extremal index for GARCH(1,1) processes
No full textGeneralised autoregressive conditional heteroskedastic (GARCH) processes have wide application in financial modelling. To characterise the extreme values of this process the extremal index is required. Existing results, which derive the analytical expression for the extremal index for the squared GARCH(1, 1) process, cannot be used to obtain the extremal index for the GARCH(1, 1) process. For the squared GARCH(1, 1) process with symmetric innovations with continuous density function and satisfying a finite moment condition, we derive an alternative analytical expression for the extremal index and new results for the limiting distribution of the size of clusters of extremes. Using these results we obtain an analytical expression for the extremal index of the GARCH(1, 1) process and an algorithm for the evaluation of properties of other cluster functionals and risk measures. We tabulate the extremal index of the GARCH(1, 1) process when the innovations are Student-t and Gaussian distributed
Extreme values in the dock.
No full textOn 9th September 1980 the bulk carrier M. V. Derbyshire sank in the Pacific Ocean, around 350 miles south-east of Japan, when she was caught in Typhoon Orchid while transporting iron ore from Canada to Japan. All 44 people on board died. Janet Heffernan and Jonathan Tawn describe their involvement as statistical expert witnesses in the Investigation of the sinking and their experience of giving evidence in court, outlining their statistical analysis which provided new insight into the circumstances surrounding the loss of the ship
Statistical models for over-dispersion in the frequency of peaks over threshold data for a flow series.
No full textIn a peaks over threshold analysis of a series of river flows, a sufficiently high threshold is used to extract the peaks of independent flood events. This paper reviews existing, and proposes new, statistical models for both the annual counts of such events and the process of event peak times. The most common existing model for the process of event times is a homogeneous Poisson process. This model is motivated by asymptotic theory. However, empirical evidence suggests that it is not the most appropriate model, since it implies that the mean and variance of the annual counts are the same, whereas the counts appear to be overdispersed, i.e., have a larger variance than mean. This paper describes how the homogeneous Poisson process can be extended to incorporate time variation in the rate at which events occur and so help to account for overdispersion in annual counts through the use of regression and mixed models. The implications of these new models on the implied probability distribution of the annual maxima are also discussed. The models are illustrated using a historical flow series from the River Thames at Kingston
Regular variation and extremal dependence of GARCH residuals with application to market risk measures
No full textStock returns exhibit heavy tails and volatility clustering. These features, motivating the
use of GARCH models, make it difficult to predict times and sizes of losses that might occur.
Estimation of losses, like the Value-at-Risk, often assume that returns, normalized by the level of
volatility, are Gaussian. Often under ARMA-GARCH modeling, such scaled returns are heavy
tailed and show extremal dependence, whose strength reduces when increasing extreme levels.
We model heavy tails of scaled returns with generalized Pareto distributions, while extremal
dependence can be reduced by declustering data
Accounting for choice of measurement scale in extreme value modeling
No full textWe investigate the effect that the choice of measurement scale has upon inference and extrapolation in extreme value analysis. Separate analyses of variables from a single process on scales which are linked by a nonlinear transformation may lead to discrepant conclusions concerning the tail behavior of the process. We propose the use of a Box–Cox power transformation incorporated as part of the inference procedure to account parametrically for the uncertainty surrounding the scale of extrapolation. This has the additional feature of increasing the rate of convergence of the distribution tails to an extreme value form in certain cases and thus reducing bias in the model estimation. Inference without reparameterization is practicably infeasible, so we explore a reparameterization which exploits the asymptotic theory of normalizing constants required for nondegenerate limit distributions. Inference is carried out in a Bayesian setting, an advantage of this being the availability of posterior predictive return levels. The methodology is illustrated on both simulated data and significant wave height data from the North Sea
Estimation of the conditional distribution of a vector variable given that one of its components is large : additional constraints for the Heffernan and Tawn model
No full textA number of different approaches to study multivariate extremes have been developed. Arguably the most useful and flexible is the theory for the distribution of a vector variable given that one of its components is large. We build on the conditional approach of Heffernan and Tawn (2004) [13] for estimating this type of multivariate extreme property. Specifically we propose additional constraints for, and slight changes in, their model formulation. These changes in the method are aimed at overcoming complications that have been experienced with using the approach in terms of their modelling of negatively associated variables, parameter identifiability problems and drawing conditional inferences which are inconsistent with the marginal distributions. The benefits of the methods are illustrated using river flow data from two tributaries of the River Thames in the UK
Jonathan Ned Katz Author Event: The Daring Life and Dangerous Times of Eve Adam
No full text“The Daring Life and Dangerous Times of Eve Adams,” interview with author, Jonathan Ned Katz, moderated by Emily Weiner (WWU) and organized by Congregation Beth Israel
Contemporary Literature. Analysis of Jonathan Bazzi's novels
No full textopenDopo una breve panoramica della letteratura italiana degli ultimi vent’anni si analizzano i due romanzi di Jonathan Bazzi "Febbre" e "Corpi minori" dai punti di vista formale, stilistico e tematico. Si discute inoltre il rapporto tra social media, autofiction e autore; nel capitolo 4 si riporta l'intervista che Bazzi ci ha gentilmente concesso, in cui questi argomenti vengono ripresi.
Si individuano alcune differenze che i testi mostrano rispetto alla letteratura moderna, e gli aspetti che hanno in comune con quella contemporanea; nel fare questo si accennano quindi alcune caratteristiche della società che li ha prodotti.The paper starts off with a brief overview of the contemporary Italian literature; then the reader is guided through an analysis of Jonathan Bazzi's novels, "Febbre" ("Fever") and "Corpi minori" ("Minor bodies"), both translated in English and published by Scribe. The relationship between author, autofiction and social media will also be discussed; in chapter four the reader will find the interview Bazzi kindly granted us
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