IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1204.3786.html
   My bibliography  Save this paper

Comparison results for Garch processes

Author

Listed:
  • Fabio Bellini
  • Franco Pellerey
  • Carlo Sgarra
  • Salimeh Yasaei Sekeh

Abstract

We consider the problem of stochastic comparison of general Garch-like processes, for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the Garch process itself, and discuss their interpretations. We focus on the convex order and show that in the case of symmetric innovations it is also propagated to the cumulated sums of the Garch process. More generally, we discuss multivariate comparison results related to the multivariate convex and supermodular order. Finally we discuss ordering with respect to the parameters in the Garch (1,1) case. Key words: Garch, Convex Order, Peakedness, Kurtosis, Supermodularity.

Suggested Citation

  • Fabio Bellini & Franco Pellerey & Carlo Sgarra & Salimeh Yasaei Sekeh, 2012. "Comparison results for Garch processes," Papers 1204.3786, arXiv.org.
    • Handle: RePEc:arx:papers:1204.3786
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1204.3786
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Ludolf E. Meester & J. George Shanthikumar, 1999. "Stochastic Convexity on General Space," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 472-494, May.
    4. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April.
    5. 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)

    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. 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).
    2. P. Kearns & A.R. Pagan, 1993. "Australian Stock Market Volatility: 1875–1987," The Economic Record, The Economic Society of Australia, vol. 69(2), pages 163-178, June.
    3. Conrad, Christian & Mammen, Enno, 2016. "Asymptotics for parametric GARCH-in-Mean models," Journal of Econometrics, Elsevier, vol. 194(2), pages 319-329.
    4. Andrea Bucci, 2020. "Realized Volatility Forecasting with Neural Networks," Journal of Financial Econometrics, Oxford University Press, vol. 18(3), pages 502-531.
    5. Jon Michel, 2020. "The Limiting Distribution of a Non‐Stationary Integer Valued GARCH(1,1) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 351-356, March.
    6. Charles, Amélie, 2010. "The day-of-the-week effects on the volatility: The role of the asymmetry," European Journal of Operational Research, Elsevier, vol. 202(1), pages 143-152, April.
    7. McMillan, David G. & Speight, Alan E. H., 2001. "Non-ferrous metals price volatility: a component analysis," Resources Policy, Elsevier, vol. 27(3), pages 199-207, September.
    8. William Miles, 2011. "Long-Range Dependence in U.S. Home Price Volatility," The Journal of Real Estate Finance and Economics, Springer, vol. 42(3), pages 329-347, April.
    9. Drost, F.C. & Klaasens, C.A.J. & Werker, B.J.M., 1994. "Adaptive Estimation in Time Series Models," Papers 9488, Tilburg - Center for Economic Research.
    10. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.
    11. Storti, G., 2006. "Minimum distance estimation of GARCH(1,1) models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1803-1821, December.
    12. Trapero, Juan R. & Cardós, Manuel & Kourentzes, Nikolaos, 2019. "Empirical safety stock estimation based on kernel and GARCH models," Omega, Elsevier, vol. 84(C), pages 199-211.
    13. LINTON, Olivier & PERRON, Benoît, 1999. "The Shape of the Risk Premium: Evidence from a Semiparametric Garch Model," Cahiers de recherche 9911, Universite de Montreal, Departement de sciences economiques.
    14. Hematizadeh, Roksana & Tajaddini, Reza, 2024. "A state-dependent international CAPM for partially integrated markets: Using local and US risk factors," Global Finance Journal, Elsevier, vol. 62(C).
    15. David McMillan & Alan Speight, 2006. "Heterogeneous information flows and intra-day volatility dynamics: evidence from the UK FTSE-100 stock index futures market," Applied Financial Economics, Taylor & Francis Journals, vol. 16(13), pages 959-972.
    16. Francq, Christian & Zakoian, Jean-Michel, 2013. "Inference in non stationary asymmetric garch models," MPRA Paper 44901, University Library of Munich, Germany.
    17. Hwang, Eunju & Jeon, ChanHyeok, 2024. "Nonnegative GARCH-type models with conditional Gamma distributions and their applications," Computational Statistics & Data Analysis, Elsevier, vol. 198(C).
    18. Sun, Yiguo & Stengos, Thanasis, 2006. "Semiparametric efficient adaptive estimation of asymmetric GARCH models," Journal of Econometrics, Elsevier, vol. 133(1), pages 373-386, July.
    19. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    20. Köksal, Bülent, 2009. "A Comparison of Conditional Volatility Estimators for the ISE National 100 Index Returns," MPRA Paper 30510, University Library of Munich, Germany.

    More about this item

    Keywords

    garch; convex order; peakedness; kurtosis; supermodularity.;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1204.3786. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.