IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v49y2022i2p681-717.html
   My bibliography  Save this article

Moment‐based estimation for the multivariate COGARCH(1,1) process

Author

Listed:
  • Thiago do Rêgo Sousa
  • Robert Stelzer

Abstract

For the multivariate COGARCH process, we obtain explicit expressions for the second‐order structure of the “squared returns” process observed on an equidistant grid. Based on this, we present a generalized method of moments estimator for its parameters. Under appropriate moment and strong mixing conditions, we show that the resulting estimator is consistent and asymptotically normal. Sufficient conditions for strong mixing, stationarity and identifiability of the model parameters are discussed in detail. We investigate the finite sample behavior of the estimator in a simulation study.

Suggested Citation

  • Thiago do Rêgo Sousa & Robert Stelzer, 2022. "Moment‐based estimation for the multivariate COGARCH(1,1) process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 681-717, June.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:2:p:681-717
    DOI: 10.1111/sjos.12531
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12531
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12531?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Enrico Bibbona & Ilia Negri, 2015. "Higher Moments and Prediction-Based Estimation for the COGARCH(1,1) Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 891-910, December.
    2. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    3. Behme, Anita, 2012. "Moments of MGOU processes and positive semidefinite matrix processes," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 183-197.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    6. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
    7. S. Haug & C. Klüppelberg & A. Lindner & M. Zapp, 2007. "Method of moment estimation in the COGARCH(1,1) model," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 320-341, July.
    8. Ross A. Maller & Gernot Muller & Alex Szimayer, 2008. "GARCH modelling in continuous time for irregularly spaced time series data," Papers 0805.2096, arXiv.org.
    9. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
    10. 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)

    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. Xiufeng Yan, 2021. "Autoregressive conditional duration modelling of high frequency data," Papers 2111.02300, arXiv.org.
    3. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    4. Inoua, Sabiou M. & Smith, Vernon L., 2023. "A classical model of speculative asset price dynamics," Journal of Behavioral and Experimental Finance, Elsevier, vol. 37(C).
    5. Tzouras, Spilios & Anagnostopoulos, Christoforos & McCoy, Emma, 2015. "Financial time series modeling using the Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 425(C), pages 50-68.
    6. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    7. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
    8. Haas, Markus & Mittnik, Stefan, 2008. "Multivariate regimeswitching GARCH with an application to international stock markets," CFS Working Paper Series 2008/08, Center for Financial Studies (CFS).
    9. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    10. Marín Díazaraque, Juan Miguel & Rodríguez Bernal, M. T. & Romero, Eva, 2013. "Data cloning estimation of GARCH and COGARCH models," DES - Working Papers. Statistics and Econometrics. WS ws132723, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Chrétien, Stéphane & Ortega, Juan-Pablo, 2014. "Multivariate GARCH estimation via a Bregman-proximal trust-region method," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 210-236.
    12. Anatolyev Stanislav, 2019. "Volatility filtering in estimation of kurtosis (and variance)," Dependence Modeling, De Gruyter, vol. 7(1), pages 1-23, February.
    13. Lee, Oesook, 2012. "V-uniform ergodicity of a continuous time asymmetric power GARCH(1,1) model," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 812-817.
    14. Kovačić, Zlatko, 2007. "Forecasting volatility: Evidence from the Macedonian stock exchange," MPRA Paper 5319, University Library of Munich, Germany.
    15. Zeynel Abidin Ozdemir, 2010. "Dynamics Of Inflation, Output Growth And Their Uncertainty In The Uk: An Empirical Analysis," Manchester School, University of Manchester, vol. 78(6), pages 511-537, December.
    16. Chia-Lin Chang & Tai-Lin Hsieh & Michael McAleer, 2016. "Connecting VIX and Stock Index ETF," Tinbergen Institute Discussion Papers 16-010/III, Tinbergen Institute, revised 23 Jan 2017.
    17. Chia-Lin Chang & Yiying Li & Michael McAleer, 2018. "Volatility Spillovers between Energy and Agricultural Markets: A Critical Appraisal of Theory and Practice," Energies, MDPI, vol. 11(6), pages 1-19, June.
    18. Zou, Yongjie & Li, Honggang, 2014. "Time spans between price maxima and price minima in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 303-309.
    19. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663.
    20. Kei Nakagawa & Yusuke Uchiyama, 2020. "GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio," Mathematics, MDPI, vol. 8(11), pages 1-12, November.

    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:bla:scjsta:v:49:y:2022:i:2:p:681-717. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.