3. Fractionally Integrated ARCH Models

  1. Evdokia Xekalaki and
  2. Stavros Degiannakis

Published Online: 31 MAR 2010

DOI: 10.1002/9780470688014.ch3

ARCH Models for Financial Applications

ARCH Models for Financial Applications

How to Cite

Xekalaki, E. and Degiannakis, S. (2010) Fractionally Integrated ARCH Models, in ARCH Models for Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470688014.ch3

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



  • autocorrelation;
  • fractionally integrated ARCH models;
  • standardized residuals;
  • volatility dynamics


Motivated by the fractionally integrated autoregressive moving average, or ARFIMA, model, Baillie et al. (1996a) proposed the fractionally integrated generalized autoregressive conditional heteroscedasticity, or FIGARCH, model. This chapter provides estimation of six fractionally integrated ARCH specifications for the FTSE100 equity index: FIGARCH, FIGARCHC, FIEGARCH, FIAPARCH, FIAPARCHC and HYGARCH. The autocorrelations for the absolute log-returns of the FTSE100 and S&P500 equity indices, the US dollar to British pound exchange rate and the price of a troy ounce of gold bullion are presented in the chapter. This chapter presents the models, which provides a description of the volatility dynamics. For instance, the FIAPARCH specification takes into consideration the leverage effect, the long memory in conditional variance and the Box–Cox power transformation of the fractionally integrated volatility. The autocorrelations for the absolute standardized residuals of the AR(0)-FIAPARCH(1,1) model are also presented in the chapter.

Controlled Vocabulary Terms

autocorrelation; autoregressive conditional heteroskedasticity