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Dynamic models for volatility and heavy tails
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ISSN: 20592507 ISBN: 9781107034723 9781107630024 9781139540933 1107630029 1107034728 1107327121 1107333563 1107335221 1107336880 1139540939 Year: 2013 Volume: 52 Publisher: Cambridge Cambridge University Press

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The volatility of financial returns changes over time and, for the last thirty years, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have provided the principal means of analyzing, modeling and monitoring such changes. Taking into account that financial returns typically exhibit heavy tails - that is, extreme values can occur from time to time - Andrew Harvey's new book shows how a small but radical change in the way GARCH models are formulated leads to a resolution of many of the theoretical problems inherent in the statistical theory. The approach can also be applied to other aspects of volatility. The more general class of Dynamic Conditional Score models extends to robust modeling of outliers in the levels of time series and to the treatment of time-varying relationships. The statistical theory draws on basic principles of maximum likelihood estimation and, by doing so, leads to an elegant and unified treatment of nonlinear time-series modeling.

Forecasting, structural time series models, and the Kalman filter
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ISBN: 0521405734 0521321964 1139881744 1107713013 1107714559 1107049997 1107715903 1107712661 1107720036 9780521405737 9781107720039 9781107049994 9781107715905 9781107714557 9780521321969 Year: 1989 Publisher: Cambridge Cambridge University Press

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In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.


Book
Dynamic models for volatility and heavy tails
Author:
ISBN: 1107327121 1107336880 1107333563 1107335221 1139540939 1107034728 1107630029 9781107336889 9781139540933 9781107335226 9781107034723 9781107630024 9781107333567 Year: 2013 Publisher: Cambridge New York

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Abstract

The volatility of financial returns changes over time and, for the last thirty years, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have provided the principal means of analyzing, modeling and monitoring such changes. Taking into account that financial returns typically exhibit heavy tails - that is, extreme values can occur from time to time - Andrew Harvey's new book shows how a small but radical change in the way GARCH models are formulated leads to a resolution of many of the theoretical problems inherent in the statistical theory. The approach can also be applied to other aspects of volatility. The more general class of Dynamic Conditional Score models extends to robust modeling of outliers in the levels of time series and to the treatment of time-varying relationships. The statistical theory draws on basic principles of maximum likelihood estimation and, by doing so, leads to an elegant and unified treatment of nonlinear time-series modeling.

State space and unobserved component models
Authors: --- --- ---
ISBN: 052183595X 1107407435 0511617011 0511889437 9780521835954 9780511617010 9781107407435 Year: 2004 Publisher: Cambridge Cambridge University Press

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This 2004 volume offers a broad overview of developments in the theory and applications of state space modeling. With fourteen chapters from twenty-three contributors, it offers a unique synthesis of state space methods and unobserved component models that are important in a wide range of subjects, including economics, finance, environmental science, medicine and engineering. The book is divided into four sections: introductory papers, testing, Bayesian inference and the bootstrap, and applications. It will give those unfamiliar with state space models a flavour of the work being carried out as well as providing experts with valuable state of the art summaries of different topics. Offering a useful reference for all, this accessible volume makes a significant contribution to the literature of this discipline.

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