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Estimation in Conditionally Heteroscedastic Time Series Models

  • Book
  • © 2005

Overview

Authors:
  1. Daniel Straumann

    1. Zürich, Switzerland

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Part of the book series: Lecture Notes in Statistics (LNS, volume 181)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction

    Pages 1-12

  3. Some Mathematical Tools

    Pages 13-36

  4. Financial Time Series: Facts and Models

    Pages 37-62

  5. Parameter Estimation: An Overview

    Pages 63-83

  6. Quasi Maximum Likelihood Estimation in Conditionally Heteroscedastic Time Series Models: A Stochastic Recurrence Equations Approach

    Pages 85-140

  7. Maximum Likelihood Estimation in Conditionally Heteroscedastic Time Series Models

    Pages 141-168

  8. Quasi Maximum Likelihood Estimation in a Generalized Conditionally Heteroscedastic Time Series Model with Heavy—tailed Innovations

    Pages 169-186

  9. Whittle Estimation in a Heavy—tailed GARCH(1,1) Model

    Pages 187-213

  10. Back Matter

    Pages 215-230
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Keywords

About this book

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 Nowadays ARCH has been replaced by more general and more sophisticated models, such as GARCH (generalized autoregressive heteroscedastic).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.

Reviews

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)

Authors and Affiliations

  • Zürich, Switzerland

    Daniel Straumann

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