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Lecture Notes in Statistics

Estimation in Conditionally Heteroscedastic Time Series Models

Authors: Straumann, Daniel

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 Nowadays ARCH has been replaced by more general and more sophisticated models, such as GARCH (generalized autoregressive heteroscedastic).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


Table of contents (8 chapters)

Table of contents (8 chapters)
  • Introduction

    Pages 1-12

  • Some Mathematical Tools

    Pages 13-36

  • Financial Time Series: Facts and Models

    Pages 37-62

  • Parameter Estimation: An Overview

    Pages 63-83

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

    Pages 85-140

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-3-540-26978-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $119.99
price for USA in USD
  • ISBN 978-3-540-21135-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Estimation in Conditionally Heteroscedastic Time Series Models
Authors
Series Title
Lecture Notes in Statistics
Series Volume
181
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-26978-6
DOI
10.1007/b138400
Softcover ISBN
978-3-540-21135-8
Series ISSN
0930-0325
Edition Number
1
Number of Pages
XVI, 228
Topics