IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2008i1p1-16.html
   My bibliography  Save this article

Mixture periodic autoregressive conditional heteroskedastic models

Author

Listed:
  • Bentarzi, M.
  • Hamdi, F.

Abstract

Mixture Periodically Correlated Autoregressive Conditionally Heteroskedastic (MPARCH) model, which extends the ARCH model, is proposed. The primary motivation behind this extension is to make the model consistent with high kurtosis, outliers and extreme events, and at the same time, able to capture the periodicity feature exhibited by the autocovariance structure. The second and the fourth moment periodically stationary conditions and their closed-forms are derived. Maximum likelihood estimation is obtained via the iterative Expectation Maximization algorithm and the performance of this algorithm is shown via a simulation studies and the MPARCH models are fitted to a real data set.

Suggested Citation

  • Bentarzi, M. & Hamdi, F., 2008. "Mixture periodic autoregressive conditional heteroskedastic models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 1-16, September.
  • Handle: RePEc:eee:csdana:v:53:y:2008:i:1:p:1-16
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00323-X
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shao, Q., 2006. "Mixture periodic autoregressive time series models," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 609-618, March.
    2. Bauwens, L. & Hafner, C.M. & Rombouts, J.V.K., 2007. "Multivariate mixed normal conditional heteroskedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3551-3566, April.
    3. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Ausin, Maria Concepcion & Galeano, Pedro, 2007. "Bayesian estimation of the Gaussian mixture GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2636-2652, February.
    6. C. S. Wong & W. K. Li, 2000. "On a mixture autoregressive model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 95-115.
    7. Zhiqiang Zhang & Wai Keung Li & Kam Chuen Yuen, 2006. "On a Mixture GARCH Time‐Series Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 577-597, July.
    8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    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. Nadia Boussaha & Faycal Hamdi & Saïd Souam, 2018. "Multivariate Periodic Stochastic Volatility Models: Applications to Algerian dinar exchange rates and oil prices modeling," EconomiX Working Papers 2018-14, University of Paris Nanterre, EconomiX.
    2. Nadia Boussaha & Faycal Hamdi & Saïd Souam, 2018. "Multivariate Periodic Stochastic Volatility Models: Applications to Algerian dinar exchange rates and oil prices modeling," Working Papers hal-04141780, HAL.
    3. Abdelhakim Aknouche & Nadia Rabehi, 2010. "On an independent and identically distributed mixture bilinear time‐series model," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 113-131, March.

    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. Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2009. "Asymmetric multivariate normal mixture GARCH," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2129-2154, April.
    2. Fayçal Hamdi & Saïd Souam, 2018. "Mixture periodic GARCH models: theory and applications," Empirical Economics, Springer, vol. 55(4), pages 1925-1956, December.
    3. Kai Yang & Qingqing Zhang & Xinyang Yu & Xiaogang Dong, 2023. "Bayesian inference for a mixture double autoregressive model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 188-207, May.
    4. Diongue, Abdou Kâ & Guégan, Dominique, 2007. "The stationary seasonal hyperbolic asymmetric power ARCH model," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1158-1164, June.
    5. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    6. Aknouche, Abdelhakim & Demmouche, Nacer & Touche, Nassim, 2018. "Bayesian MCMC analysis of periodic asymmetric power GARCH models," MPRA Paper 91136, University Library of Munich, Germany.
    7. Xiufeng Yan, 2021. "Autoregressive conditional duration modelling of high frequency data," Papers 2111.02300, arXiv.org.
    8. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    9. Wang, Hui & Pan, Jiazhu, 2014. "Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 117-123.
    10. Francesco Audrino & Fabio Trojani, 2006. "Estimating and predicting multivariate volatility thresholds in global stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 345-369, April.
    11. Massimiliano Caporin & Francesco Poli, 2017. "Building News Measures from Textual Data and an Application to Volatility Forecasting," Econometrics, MDPI, vol. 5(3), pages 1-46, August.
    12. Bernd Hayo & Ali M. Kutan, 2005. "The impact of news, oil prices, and global market developments on Russian financial markets," The Economics of Transition, The European Bank for Reconstruction and Development, vol. 13(2), pages 373-393, April.
    13. Fresoli, Diego E. & Ruiz, Esther, 2016. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 170-185.
    14. Rombouts, Jeroen V.K. & Stentoft, Lars, 2011. "Multivariate option pricing with time varying volatility and correlations," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2267-2281, September.
    15. Hayo, Bernd & Kutan, Ali M., 2005. "IMF-related news and emerging financial markets," Journal of International Money and Finance, Elsevier, vol. 24(7), pages 1126-1142, November.
    16. Xiufeng Yan, 2021. "Multiplicative Component GARCH Model of Intraday Volatility," Papers 2111.02376, arXiv.org.
    17. Regnard, Nazim & Zakoïan, Jean-Michel, 2011. "A conditionally heteroskedastic model with time-varying coefficients for daily gas spot prices," Energy Economics, Elsevier, vol. 33(6), pages 1240-1251.
    18. Raunig, Burkhard, 2006. "The longer-horizon predictability of German stock market volatility," International Journal of Forecasting, Elsevier, vol. 22(2), pages 363-372.
    19. Carol Alexander & Emese Lazar, 2009. "Modelling Regime‐Specific Stock Price Volatility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(6), pages 761-797, December.
    20. Souza, Leonardo & Veiga, Alvaro & Medeiros, Marcelo C., 2005. "Evaluating the Forecasting Performance of GARCH Models Using White’s Reality Check," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 25(1), May.

    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:eee:csdana:v:53:y:2008:i:1:p:1-16. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.