Estimation in conditionally heteroscedastic time series models
Author(s)
Bibliographic Information
Estimation in conditionally heteroscedastic time series models
（Lecture notes in statistics, Bd. 181）
Springer, c2005
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Note
Originally presented as the author's thesis (Ph.D.)--RiskLab, Department of Mathematics, ETH Zürich
Includes bibliographical references (p. [215]-220) and indexes
Description and Table of Contents
Description
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 Nowadays ARCH has been replaced by more general and more sophisticated models, such as GARCH (generalized autoregressive heteroscedastic).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.
Table of Contents
Some Mathematical Tools.- Financial Time Series: Facts and Models.- Parameter Estimation: An Overview.- Quasi Maximum Likelihood Estimation in Conditionally Heteroscedastic Time Series Models: A Stochastic Recurrence Equations Approach.- Maximum Likelihood Estimation in Conditionally Heteroscedastic Time Series Models.- Quasi Maximum Likelihood Estimation in a Generalized Conditionally Heteroscedastic Time Series Model with Heavy-tailed Innovations.- Whittle Estimation in a Heavy-tailed GARCH(1,1) Model.
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