IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i18p3262-3268.html
   My bibliography  Save this article

On the existence of higher-order moments of periodic GARCH models

Author

Listed:
  • Aknouche, Abdelhakim
  • Bentarzi, Mohamed

Abstract

In this paper we mainly study the existence of higher-order moments of periodic GARCH models (P-GARCH) introduced by [Bollerslev, T., Ghysels, E., 1996. Periodic autoregressive conditional heteroskedasticity. Journal of Business and Economic Statistics 14, 139-152]. We provide an explicit necessary and sufficient condition for the existence of higher-order moments for a general P-GARCHS(p,q) model. Our main result generalizes the necessary and sufficient moment condition recently obtained by [Ling, S., McAleer, M., 2002a. Stationarity and the existence of moments of a family of GARCH processes. Journal of Econometrics 106, 109-117; Ling, S., McAleer, M., 2002b. Necessary and sufficient moment conditions for the GARCH(p,q) and asymmetric power GARCH(p,q) models. Econometric Theory 18, 722-729] for the classical GARCH(p,q) models.

Suggested Citation

  • Aknouche, Abdelhakim & Bentarzi, Mohamed, 2008. "On the existence of higher-order moments of periodic GARCH models," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3262-3268, December.
  • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3262-3268
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00311-8
    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. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    2. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(3), pages 722-729, June.
    3. Philip Hans Franses & Richard Paap, 2000. "Modelling day-of-the-week seasonality in the S&P 500 index," Applied Financial Economics, Taylor & Francis Journals, vol. 10(5), pages 483-488.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Mohamed Bentarzi & Marc Hallin, 1994. "On The Invertibility Of Periodic Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 263-268, May.
    6. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(1), pages 232-261, February.
    7. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
    8. Bentarzi, Mohamed, 1998. "Model-Building Problem of Periodically Correlatedm-Variate Moving Average Processes," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 1-21, July.
    9. repec:bla:jecsur:v:16:y:2002:i:3:p:245-69 is not listed on IDEAS
    10. W. K. Li & Shiqing Ling & Michael McAleer, 2002. "Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 245-269, July.
    11. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    12. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    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. Abdelhakim Aknouche & Eid Al-Eid, 2012. "Asymptotic inference of unstable periodic ARCH processes," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 61-79, April.
    2. Sigauke, C. & Chikobvu, D., 2011. "Prediction of daily peak electricity demand in South Africa using volatility forecasting models," Energy Economics, Elsevier, vol. 33(5), pages 882-888, September.
    3. Fayçal Hamdi & Saïd Souam, 2018. "Mixture periodic GARCH models: theory and applications," Empirical Economics, Springer, vol. 55(4), pages 1925-1956, 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. McAleer, Michael & Chan, Felix & Marinova, Dora, 2007. "An econometric analysis of asymmetric volatility: Theory and application to patents," Journal of Econometrics, Elsevier, vol. 139(2), pages 259-284, August.
    2. Li, Ming-Yuan Leon, 2008. "Clarifying the dynamics of the relationship between option and stock markets using the threshold vector error correction model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 511-520.
    3. Massimiliano Caporin & Michael McAleer, 2010. "Model Selection and Testing of Conditional and Stochastic Volatility Models," KIER Working Papers 724, Kyoto University, Institute of Economic Research.
    4. Ping-Yu Chen & Chia-Lin Chang & Chi-Chung Chen & Michael McAleer, 2010. "Modeling the Effect of Oil Price on Global Fertilizer Prices," Working Papers in Economics 10/55, University of Canterbury, Department of Economics and Finance.
    5. Suhejla Hoti & Felix Chan & Michael McAleer, 2003. "Structure and Asymptotic Theory for Multivariate Asymmetric Volatility: Empirical Evidence for Country Risk Ratings," CIRJE F-Series CIRJE-F-203, CIRJE, Faculty of Economics, University of Tokyo.
    6. Chia-Lin Chang & Michael McAleer & Christine Lim, 2010. "Modelling the Volatility in Short and Long Haul Japanese Tourist Arrivals to New Zealand and Taiwan," Working Papers in Economics 10/40, University of Canterbury, Department of Economics and Finance.
    7. Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & McAleer, Michael & Amaral, Teodosio Perez, 2013. "The rise and fall of S&P500 variance futures," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 151-167.
    8. Chia-Lin Chang & Michael Mcaleer, 2009. "Daily Tourist Arrivals, Exchange Rates and Voatility for Korea and Taiwan," Korean Economic Review, Korean Economic Association, vol. 25, pages 241-267.
    9. Casarin, Roberto & Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & McAleer, Michael & Pérez-Amaral, Teodosio, 2013. "Risk management of risk under the Basel Accord: A Bayesian approach to forecasting Value-at-Risk of VIX futures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 183-204.
    10. Divino, Jose Angelo & McAleer, Michael, 2010. "Modelling and forecasting daily international mass tourism to Peru," Tourism Management, Elsevier, vol. 31(6), pages 846-854.
    11. Watkins, Clinton & McAleer, Michael, 2008. "How has volatility in metals markets changed?," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(2), pages 237-249.
    12. Lan-Fen Chu & Michael McAleer & Chi-Chung Chen, 2012. "How Volatile is ENSO for Global Greenhouse Gas Emissions and the Global Economy?," Journal of Reviews on Global Economics, Lifescience Global, vol. 1, pages 1-12.
    13. McAleer, M.J. & Jiménez-Martín, J.A. & Pérez-Amaral, T., 2008. "A decision rule to minimize daily capital charges in forecasting value-at-risk," Econometric Institute Research Papers EI 2008-34, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    14. McAleer, Michael & Jimenez-Martin, Juan-Angel & Perez-Amaral, Teodosio, 2013. "Has the Basel Accord improved risk management during the global financial crisis?," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 250-265.
    15. Abdul Hakim & Michael McAleer, 2010. "Modelling the interactions across international stock, bond and foreign exchange markets," Applied Economics, Taylor & Francis Journals, vol. 42(7), pages 825-850.
    16. Chia-Lin Chang & Michael Mcaleer, 2012. "Aggregation, Heterogeneous Autoregression And Volatility Of Daily International Tourist Arrivals And Exchange Rates," The Japanese Economic Review, Japanese Economic Association, vol. 63(3), pages 397-419, September.
    17. Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Michael McAleer & Teodosio Pérez-Amaral, 2011. "Risk Management of Risk under the Basel Accord: Forecasting Value-at-Risk of VIX Futures," Documentos de Trabajo del ICAE 2011-02, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    18. Michael McAleer & Juan‐Ángel Jiménez‐Martín & Teodosio Pérez‐Amaral, 2013. "International Evidence on GFC‐Robust Forecasts for Risk Management under the Basel Accord," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(3), pages 267-288, April.
    19. Dora Marinova & Michael McAleer, 2002. "Trends and volatility in Japanese patenting in the USA: An analysis of the electronics and transport industries," Scientometrics, Springer;Akadémiai Kiadó, vol. 55(2), pages 171-187, August.
    20. Jimenez-Martin, Juan-Angel & McAleer, Michael & Pérez-Amaral, Teodosio & Santos, Paulo Araújo, 2013. "GFC-robust risk management under the Basel Accord using extreme value methodologies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 223-237.

    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:stapro:v:78:y:2008:i:18:p:3262-3268. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.