Estimation in Conditionally Heteroscedastic Time Series Models

By: Daniel Straumann

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Paperback | 19 November 2004

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248 Pages

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In his seminal 1982 paper, Robert F. Engle described a time series model with a time-varying volatility. Engle showed that this model, which he called ARCH (autoregressive conditionally heteroscedastic), is well-suited for the description of economic and financial price. Nowadays ARCH has been replaced by more general and more sophisticated models, such as GARCH (generalized autoregressive heteroscedastic).

This monograph concentrates on mathematical statistical problems associated with fitting conditionally heteroscedastic time series models to data. This includes the classical statistical issues of consistency and limiting distribution of estimators. Particular attention is addressed to (quasi) maximum likelihood estimation and misspecified models, along to phenomena due to heavy-tailed innovations. The used methods are based on techniques applied to the analysis of stochastic recurrence equations. Proofs and arguments are given wherever possible in full mathematical rigour. Moreover, the theory is illustrated by examples and simulation studies.

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From the reviews of the first edition:

"The book deals with conditionally heteroscedastic time series models. It covers classical and new topics of parameter estimation in such models. ... There are a lot of various examples and remarks which clarify the presented general results. Some numerical examples and simulations are given. Detailed discussions and comparisons with known results are presented in each chapter." (Andrew Olenko, Zentralblatt MATH, Vol. 1086, 2006)

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Stochastics Economics Econometrics Economic Statistics Accounting & Finance Finance Probability & Statistics Optimisation Game Theory

Introduction
Financial time series: facts and models
Some mathematical tools
Parameter estimation: an overview
The QMLE in heteroscedastic time series models: a stochastic recurrence equations approach
Maximum-likelihood estimation in conditionally heteroscedastic time series models
Whittle estimation in a heavy-tailed GARCH (1,1) model
Table of Contents provided by Publisher. All Rights Reserved.

Estimation in Conditionally Heteroscedastic Time Series Models

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Industry Reviews

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