Threshold heteroskedastic models

https://doi.org/10.1016/0165-1889(94)90039-6Get rights and content

Abstract

In this paper we consider a modification of the classical ARCH models introduced by Engle (1982). In this modified model the conditional standard deviation is a piecewise linear function of past values of the white noise. This specific form allows different reactions of the volatility to different signs of the lagged errors. Stationarity conditions are derived. Maximum likelihood and least squares estimation are also considered. Finally an empirical example relating to the French CAC stock index is presented and several specifications are compared.

References (23)

  • T. Bollerslev

    Generalized autoregressive conditional heteroskedasticity

    Journal of Econometrics

    (1986)
  • A.A. Christie

    The stochastic behavior of common stock variances

    Journal of Financial Economics

    (1982)
  • M. Abramowitz et al.

    Handbook of mathematical functions

    (1964)
  • E.K. Berndt et al.

    Estimation inference in nonlinear structural models

    Annals of Economic and Social Measurement

    (1974)
  • M. Davidian et al.

    Variance function estimation

    Journal of the American Statistical Association

    (1987)
  • R.F. Engle

    Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation

    Econometrica

    (1982)
  • R.F. Engle et al.

    Estimation of time varying risk premiums in the term structure

    Econometrica

    (1985)
  • L.R. Glosten et al.

    Relationship between the expected value and the volatility of the nominal excess return on stocks

    (1989)
  • L.J. Godfrey

    On the invariance of the Lagrange multiplier test with respect to certain changes in the alternative hypothesis

    Econometrica

    (1981)
  • C. Gouriéroux et al.

    Statistiques et modèles economètriques

    (1989)
  • C. Gouriéroux

    Modèles ARCH et applications à la finance

    (1989)
  • Cited by (1359)

    • A permutation entropy analysis of Bitcoin volatility

      2024, Physica A: Statistical Mechanics and its Applications
    View all citing articles on Scopus

    I should like to thank Christian Gouriéroux and two anonymous referees for their comments and Roger Rabemananjara for the empirical example.

    View full text