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1 - Introduction

Published online by Cambridge University Press:  05 May 2013

Andrew C. Harvey
Affiliation:
University of Cambridge
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Summary

The aim of this monograph is to set out a unified and comprehensive theory for a class of nonlinear time series models that can deal with dynamic distributions. The emphasis is on models in which the conditional distribution of an observa-tion may be heavy-tailed and the location and/or scale changes over time. The defining feature of these models is that the dynamics are driven by the score of the conditional distribution. When a suitable link function is employed for the changing parameter, analytic expressions may be derived for unconditional moments, autocorrelations and moments of multistep forecasts. Furthermore, a full asymptotic distribution theory for maximum likelihood estimators can be developed, including analytic expressions for asymptotic covariance matrices of the estimators.

The class of what we call dynamic conditional score (DCS) models includes standard linear time series models observed with an error that may be subject to outliers, models which capture changing conditional variance and models for non-negative variables. The last two of these are of considerable importance in financial econometrics, where they are used for forecasting volatility. A guiding principle underlying the proposed class of models is that of signal extraction. When combined with basic ideas of maximum likelihood estimation, the signal extraction approach leads to models which, in contrast to many in the literature, are relatively simple and yield analytic expressions for their principal features.

Type
Chapter
Information
Dynamic Models for Volatility and Heavy Tails
With Applications to Financial and Economic Time Series
, pp. 1 - 18
Publisher: Cambridge University Press
Print publication year: 2013

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  • Introduction
  • Andrew C. Harvey, University of Cambridge
  • Book: Dynamic Models for Volatility and Heavy Tails
  • Online publication: 05 May 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139540933.002
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  • Introduction
  • Andrew C. Harvey, University of Cambridge
  • Book: Dynamic Models for Volatility and Heavy Tails
  • Online publication: 05 May 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139540933.002
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Introduction
  • Andrew C. Harvey, University of Cambridge
  • Book: Dynamic Models for Volatility and Heavy Tails
  • Online publication: 05 May 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139540933.002
Available formats
×