IDEAS home Printed from https://ideas.repec.org/p/ulb/ulbeco/2013-13740.html
   My bibliography  Save this paper

The exact quasi-likelihood of time dependent ARMA models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/13740/1/ISBRUX96.pdf
    File Function: ISBRUX96
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Guy Melard, 1977. "Sur une classe de modèles ARIMA dépendant du temps," ULB Institutional Repository 2013/13676, ULB -- Universite Libre de Bruxelles.
    4. 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.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. 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.
    7. 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.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rajae Azrak & Guy Melard, 1993. "Exact maximum likelihood estimation for extended ARIMA models," ULB Institutional Repository 2013/13802, ULB -- Universite Libre de Bruxelles.
    2. André Klein & Guy Melard & Toufik Zahaf, 1998. "Computation of the exact information matrix of Gaussian dynamic regression time series models," ULB Institutional Repository 2013/13738, ULB -- Universite Libre de Bruxelles.
    3. Zijian Zeng & Meng Li, 2020. "Bayesian Median Autoregression for Robust Time Series Forecasting," Papers 2001.01116, arXiv.org, revised Dec 2020.
    4. Melard, Guy & Roy, Roch & Saidi, Abdessamad, 2006. "Exact maximum likelihood estimation of structured or unit root multivariate time series models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 2958-2986, July.
    5. Zeng, Zijian & Li, Meng, 2021. "Bayesian median autoregression for robust time series forecasting," International Journal of Forecasting, Elsevier, vol. 37(2), pages 1000-1010.
    6. Guy Melard, 1994. "Modèles linéaires et non linéaires," ULB Institutional Repository 2013/13804, ULB -- Universite Libre de Bruxelles.
    7. M. Shelton Peiris & Manabu Asai, 2016. "Generalized Fractional Processes with Long Memory and Time Dependent Volatility Revisited," Econometrics, MDPI, vol. 4(3), pages 1-21, September.
    8. 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.
    9. Karanasos, Menelaos & Paraskevopoulos,Alexandros & Canepa, Alessandra, 2020. "Unified Theory for the Large Family of Time Varying Models with Arma Representations: One Solution Fits All," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202008, University of Turin.
    10. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    11. Mauricio, Jose Alberto, 2008. "Computing and using residuals in time series models," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1746-1763, January.
    12. Beran, Jan & Feng, Yuanhua, 1999. "Local Polynomial Estimation with a FARIMA-GARCH Error Process," CoFE Discussion Papers 99/08, University of Konstanz, Center of Finance and Econometrics (CoFE).
    13. Corbet, Shaen & Larkin, Charles & McMullan, Caroline, 2020. "The impact of industrial incidents on stock market volatility," Research in International Business and Finance, Elsevier, vol. 52(C).
    14. Cho, Guedae & Kim, MinKyoung & Koo, Won W., 2003. "Relative Agricultural Price Changes In Different Time Horizons," 2003 Annual meeting, July 27-30, Montreal, Canada 22249, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    15. Minot, Nicholas, 2014. "Food price volatility in sub-Saharan Africa: Has it really increased?," Food Policy, Elsevier, vol. 45(C), pages 45-56.
    16. Umar, Muhammad & Mirza, Nawazish & Rizvi, Syed Kumail Abbas & Furqan, Mehreen, 2023. "Asymmetric volatility structure of equity returns: Evidence from an emerging market," The Quarterly Review of Economics and Finance, Elsevier, vol. 87(C), pages 330-336.
    17. Shively, Gerald E., 2001. "Price thresholds, price volatility, and the private costs of investment in a developing country grain market," Economic Modelling, Elsevier, vol. 18(3), pages 399-414, August.
    18. Lahmiri, Salim & Bekiros, Stelios, 2017. "Disturbances and complexity in volatility time series," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 38-42.
    19. Hao Chen & Qiulan Wan & Yurong Wang, 2014. "Refined Diebold-Mariano Test Methods for the Evaluation of Wind Power Forecasting Models," Energies, MDPI, vol. 7(7), pages 1-14, July.
    20. Tomanova, Lucie, 2013. "Exchange Rate Volatility and the Foreign Trade in CEEC," EY International Congress on Economics I (EYC2013), October 24-25, 2013, Ankara, Turkey 267, Ekonomik Yaklasim Association.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ulb:ulbeco:2013/13740. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Benoit Pauwels (email available below). General contact details of provider: https://edirc.repec.org/data/ecsulbe.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.