Advertisement

Quasi-maximum Likelihood Estimation of Periodic Autoregressive, Conditionally Heteroscedastic Time Series

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 122)

Abstract

We consider a general multivariate periodically stationary and ergodic causal time series model. We prove consistency and asymptotic normality of the quasi-maximum likelihood (QML) estimator of it. Applications to the multivariate nonlinear periodic AR(∞)–ARCH(∞) process are shown.

Keywords

Quasi-maximum Likelihood (QML) Periodic Autoregressive QML Estimation Time Series Models Asymptotic Normality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bardet J-M, Wintenberger O (2009) Asymptotic normality of the quasi-maximum likelihood estimator for multidimensional causal processes. Ann Stat 37(5):2730–2759 MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aknouche A, Al-Eid E (2012) Asymptotic inference of unstable periodic ARCH processes. Stat Inference Stoch Process 15:61–79 MathSciNetCrossRefGoogle Scholar
  3. 3.
    Doukhan P, Wintenberger O (2008) Weakly dependent chains with infinite memory. Stoch Process Appl 118(11):1997–2013 MathSciNetCrossRefGoogle Scholar
  4. 4.
    Aknouche A, Bibi A (2009) Quasi-maximum likelihood estimation of periodic GARCH and periodic ARMA-GARCH processes. J Time Ser Anal 40(1):19–46 MathSciNetCrossRefGoogle Scholar
  5. 5.
    Straumann D, Mikosch T (2009) Quasi-maximum likelihood estimation in conditionally heteroscedastic time series: a stochastic recurrence equations approach. Ann Stat 34(5):2449–2495 MathSciNetCrossRefGoogle Scholar
  6. 6.
    Jeantheau T (1998) Strong consistency of estimators for multivariate ARCH models. Econ Theory 14(1):70–86 MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Europa-Universität ViadrinaFrankfurt (Oder)Germany

Personalised recommendations