5. Other Distributional Assumptions

  1. Evdokia Xekalaki and
  2. Stavros Degiannakis

Published Online: 31 MAR 2010

DOI: 10.1002/9780470688014.ch5

ARCH Models for Financial Applications

ARCH Models for Financial Applications

How to Cite

Xekalaki, E. and Degiannakis, S. (2010) Other Distributional Assumptions, in ARCH Models for Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470688014.ch5

Author Information

  1. Department of Statistics Athens University of Economics and Business, Greece

Publication History

  1. Published Online: 31 MAR 2010
  2. Published Print: 16 APR 2010

ISBN Information

Print ISBN: 9780470066300

Online ISBN: 9780470688014



  • ARCH models;
  • Bayesian estimation;
  • distributional assumptions;
  • EViews;
  • non-normally distributed standardized innovations


An attractive feature of the ARCH process is that even though the conditional distribution of the innovations is normal, the unconditional distribution has thicker tails than the normal distribution. This chapter deals with the estimation of three conditional volatility models that capture the main characteristics of asset returns under three distributional assumptions for the S&P500 equity index. It presents the models that describe the volatility dynamics adequately. EViews 6 provides the option to estimate an ARCH model assuming that the standardized residuals follow the normal, Student’s t or the generalized error distribution. The volatility specifications provided by EViews are estimated for p = q = 1: GARCH(1,1), IGARCH(1,1), EGARCH(1,1), APARCH(1,1), GRJ(1,1), CGARCH(1,1) and ACGARCH(1,1). The conditional mean is considered as a first order autoregressive process. Thus, seven conditional volatility models under three distributional assumptions are defined.

Controlled Vocabulary Terms

autoregressive conditional heteroskedasticity; Bayes estimator; Student's t-test