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The exact quasi-likelihood of time dependent ARMA models

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  • Rajae Azrak
  • Guy Melard

Abstract

The purpose of the paper is to propose a simple and efficient algorithm to evaluate the exact quasi-likelihood of (possibly marginally heteroscedastic) ARMA models with time-dependent coefficients. The algorithm is based on the Kalman filter and is therefore simpler than a previous algorithm based on a Cholesky factorisation. Computational efficiency is obtained by taking the ARMA structure into account. Empirical evidence is given.

Suggested Citation

  • Rajae Azrak & Guy Melard, 1998. "The exact quasi-likelihood of time dependent ARMA models," ULB Institutional Repository 2013/13740, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/13740
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    References listed on IDEAS

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    1. Guy Melard & Roch Roy, 1988. "Modèles de séries chronologiques avec seuil," ULB Institutional Repository 2013/13706, ULB -- Universite Libre de Bruxelles.
    2. Marc Hallin, 1986. "Nonstationary q-dependent processes and time-varying moving average models: invertibility properties and the forecasting problem," ULB Institutional Repository 2013/2005, ULB -- Universite Libre de Bruxelles.
    3. Hallin, Marc, 1978. "Mixed autoregressive-moving average multivariate processes with time-dependent coefficients," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 567-572, December.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Guy Melard, 1984. "Algorithm AS197: A fast algorithm for the exact likelihood of autoregressive-moving average models," ULB Institutional Repository 2013/13692, ULB -- Universite Libre de Bruxelles.
    6. G. Gardner & A. C. Harvey & G. D. A. Phillips, 1980. "An Algorithm for Exact Maximum Likelihood Estimation of Autoregressive–Moving Average Models by Means of Kaiman Filtering," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 311-322, November.
    7. Ansley, Craig F. & Newbold, Paul, 1980. "Finite sample properties of estimators for autoregressive moving average models," Journal of Econometrics, Elsevier, vol. 13(2), pages 159-183, June.
    8. Guy Melard, 1977. "Sur une classe de modèles ARIMA dépendant du temps," ULB Institutional Repository 2013/13676, ULB -- Universite Libre de Bruxelles.
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    Cited by:

    1. Rajae Azrak & Guy Melard, 2017. "Autoregressive Models with Time-dependent Coefficients. A comparison between Several Approaches," Working Papers ECARES ECARES 2017-48, ULB -- Universite Libre de Bruxelles.
    2. Alj, Abdelkamel & Jónasson, Kristján & Mélard, Guy, 2016. "The exact Gaussian likelihood estimation of time-dependent VARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 633-644.
    3. Rajae Azrak & Guy Mélard, 2022. "Autoregressive Models with Time-Dependent Coefficients—A Comparison between Several Approaches," Stats, MDPI, vol. 5(3), pages 1-21, August.
    4. Yacouba Boubacar Maïnassara & Landy Rabehasaina, 2020. "Estimation of weak ARMA models with regime changes," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 1-52, April.
    5. Xinyang Wang & Dehui Wang & Kai Yang, 2021. "Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 713-750, July.
    6. Han Li & Kai Yang & Dehui Wang, 2017. "Quasi-likelihood inference for self-exciting threshold integer-valued autoregressive processes," Computational Statistics, Springer, vol. 32(4), pages 1597-1620, December.

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