Download or read book A Contribution to the Estimation of the Tail Index of Heavy tailed Distributions written by Bruno C. Sousa and published by . This book was released on 2002 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Robustness of Tail Index Estimation written by Ping-Hung Hsieh and published by . This book was released on 1997 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Fundamentals of Heavy Tails written by Jayakrishnan Nair and published by Cambridge University Press. This book was released on 2022-06-09 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.
Download or read book On Adaptive Tail Index Estimation for Financial Return Models written by Niklas Wagner and published by . This book was released on 2008 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimation of the tail index of stationary, fat-tailed return distributions is non-trivial since the well-known Hill estimator is optimal only under iid draws from an exact Pareto model. We provide a small sample simulation study of recently suggested adaptive estimators under ARCH-type dependence. The Hill estimator's performance is found to be dominated by a ratio estimator. Dependence increases estimation error which can remain substantial even in larger data sets. As small sample bias is related to the magnitude of the tail index, recent standard applications may have overestimated (underestimated) the risk of assets with low (high) degrees of fat-tailedness.
Download or read book Tail Index and Quantile Estimation with Very High Frequency Data written by Casper G. de Vries and published by . This book was released on 1996 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modelling Extremal Events written by Paul Embrechts and published by Springer Science & Business Media. This book was released on 2013-01-02 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A reader's first impression on leafing through this book is of the large number of graphs and diagrams, used to illustrate shapes of distributions...and to show real data examples in various ways. A closer reading reveals a nice mix of theory and applications, with the copious graphical illustrations alluded to. Such a mixture is of course dear to the heart of the applied probabilist/statistician, and should impress even the most ardent theorists." --MATHEMATICAL REVIEWS
Download or read book Continuous time Tail Index Estimation written by Florian Milanovici and published by . This book was released on 2007 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: In applications to finance, insurance, physics and many other fields, statisticians are often faced with high quality datasets that exhibit deviations from the "normal behavior", caused by the extremes in the sample. As a consequence in recent years a great deal of research has been done in heavy-tailed modelling. Although much of the existing literature focuses on the discrete-time case, the continuoustime heavy-tailed modelling is a very natural technique in many applications and therefore more attention should be paid to the continuous-time case. This is the motivation for the research in this dissertation. We will be focusing mainly on extending the Hill estimator (Hill (1975)) to estimating the tail index of continuoustime stationary stochastic processes. Since one can sample basically as many observations as possible from the continuous-time process, there is a temptation on the practitioner's part to use as large a sample as possible when applying the Hill estimator. We will show that this will lead in many instances to asymptotically inconsistent estimators. (Abstract).
Download or read book On Tail Index Estimation Using Dependent Data written by Tailen Hsing and published by . This book was released on 1989 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let X1, X2,... be possibly dependent random variables having the same marginal distribution. Consider the situation where $\bar{F}(x) := P\lbrack X_1 > x\rbrack$ is regularly varying at ∞ with an unknown index $- \alpha
Download or read book Heavy Tail Phenomena written by Sidney I. Resnick and published by Springer Science & Business Media. This book was released on 2007 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. It is uniquely devoted to heavy-tails and emphasizes both probability modeling and statistical methods for fitting models. Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use a statistics package. This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.
Download or read book Tail Index Estimation written by Jón Daníelsson and published by . This book was released on 2019 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The selection of upper order statistics in tail estimation is notoriously difficult. Methods that are based on asymptotic arguments, like minimizing the asymptotic MSE, do not perform well in finite samples. Here, we advance a data-driven method that minimizes the maximum distance between the fitted Pareto type tail and the observed quantile. To analyze the finite sample properties of the metric, we perform rigorous simulation studies. In most cases, the finite sample-based methods perform best. To demonstrate the economic relevance of choosing the proper methodology, we use daily equity return data from the CRSP database and find economically relevant variation between the tail index estimates"--Abstract.
Download or read book Asymptotic Methods in Probability and Statistics written by B. Szyszkowicz and published by Elsevier. This book was released on 1998-10-29 with total page 925 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the aims of the conference on which this book is based, was to provide a platform for the exchange of recent findings and new ideas inspired by the so-called Hungarian construction and other approximate methodologies. This volume of 55 papers is dedicated to Miklós Csörgő a co-founder of the Hungarian construction school by the invited speakers and contributors to ICAMPS'97.This excellent treatize reflects the many developments in this field, while pointing to new directions to be explored. An unequalled contribution to research in probability and statistics.
Download or read book Tail Index Estimation in Models of Generalized Order Statistics written by Frank Marohn and published by . This book was released on 2003 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tail Index Estimation written by and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Adaptive Tail Index Estimation for Financial Return Models written by Niklas F. Wagner and published by . This book was released on 2000 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tail Index Estimation for a Filtered Dependent Time Series written by Jonathan B. Hill and published by . This book was released on 2015 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove Hill's (1975) tail index estimator is asymptotically normal where the employed data are generated by a stationary parametric process {x(t)}. We assume x(t) is an unobservable function of a parameter q that is estimable. Natural applications include regression residuals and GARCH filters. Our main result extends Resnick and Stărică's (1997) theory for estimated AR i.i.d. errors and Ling and Peng's (2004) theory for estimated ARMA i.i.d. errors to a wide range of filtered time series since we do not require x(t) to be i.i.d., nor generated by a linear process with geometric dependence. We assume x(t) is b-mixing with possibly hyperbolic dependence, covering ARMA-GARCH filters, ARMA filters with heteroscedastic errors of unknown form, nonlinear filters like threshold autoregressions, and filters based on mis-specified models, as well as i.i.d. errors in an ARMA model. Finally, as opposed to existing results we do not require the plug-in for q to be super-n1/2-convergent when x(t) has an infinite variance allowing a far greater variety of plug-ins including those that are slower than n1/2 , like QML-type estimators for GARCH models.
Download or read book Estimation of the Tail Index of a Distribution written by Rudolf Grübel and published by . This book was released on 1994 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Robust Tail Index Estimation for Linear Long Memory Processes written by Jan Beran and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
