IDEAS home Printed from https://ideas.repec.org/a/jss/jstsof/v080i04.html
   My bibliography  Save this article

COGARCH(p, q): Simulation and Inference with the yuima Package

Author

Listed:
  • Iacus, Stefano M.
  • Mercuri, Lorenzo
  • Rroji, Edit

Abstract

In this paper we show how to simulate and estimate a COGARCH(p, q) model in the R package yuima. Several routines for simulation and estimation are introduced. In particular, for the generation of a COGARCH(p, q) trajectory, the user can choose between two alternative schemes. The first is based on the Euler discretization of the stochastic differential equations that identify a COGARCH(p, q) model while the second considers the explicit solution of the equations defining the variance process. Estimation is based on the matching of the empirical with the theoretical autocorrelation function. Three different approaches are implemented: minimization of the mean squared error, minimization of the absolute mean error and the generalized method of moments where the weighting matrix is continuously updated. Numerical examples are given in order to explain methods and classes used in the yuima package.

Suggested Citation

  • Iacus, Stefano M. & Mercuri, Lorenzo & Rroji, Edit, 2017. "COGARCH(p, q): Simulation and Inference with the yuima Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 80(i04).
    • Handle: RePEc:jss:jstsof:v:080:i04
    DOI: http://hdl.handle.net/10.18637/jss.v080.i04
    as

    Download full text from publisher

    File URL: https://www.jstatsoft.org/index.php/jss/article/view/v080i04/v80i04.pdf
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v080i04/yuima_1.6.8.tar.gz
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v080i04/v80i04.R
    Download Restriction: no
    File URL: https://libkey.io/http://hdl.handle.net/10.18637/jss.v080.i04?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. Dionne, Georges & Duchesne, Pierre & Pacurar, Maria, 2009. "Intraday Value at Risk (IVaR) using tick-by-tick data with application to the Toronto Stock Exchange," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 777-792, December.
    2. Shao, Xi-Dong & Lian, Yu-Jun & Yin, Lian-Qian, 2009. "Forecasting Value-at-Risk using high frequency data: The realized range model," Global Finance Journal, Elsevier, vol. 20(2), pages 128-136.
    3. Ross A. Maller & Gernot Muller & Alex Szimayer, 2008. "GARCH modelling in continuous time for irregularly spaced time series data," Papers 0805.2096, arXiv.org.
    4. Brouste, Alexandre & Fukasawa, Masaaki & Hino, Hideitsu & Iacus, Stefano & Kamatani, Kengo & Koike, Yuta & Masuda, Hiroki & Nomura, Ryosuke & Ogihara, Teppei & Shimuzu, Yasutaka & Uchida, Masayuki & Y, 2014. "The YUIMA Project: A Computational Framework for Simulation and Inference of Stochastic Differential Equations," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i04).
    5. Stefano Iacus & Lorenzo Mercuri, 2015. "Implementation of Lévy CARMA model in Yuima package," Computational Statistics, Springer, vol. 30(4), pages 1111-1141, December.
    6. Loregian, Angela & Mercuri, Lorenzo & Rroji, Edit, 2012. "Approximation of the variance gamma model with a finite mixture of normals," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 217-224.
    7. Henghsiu Tsai & K. S. Chan, 2005. "A note on non‐negative continuous time processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 589-597, September.
    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. Lorenzo Mercuri & Andrea Perchiazzo & Edit Rroji, 2020. "Finite Mixture Approximation of CARMA(p,q) Models," Papers 2005.10130, arXiv.org, revised May 2020.
    2. Mohammadi, M. & Rezakhah, S. & Modarresi, N., 2020. "Semi-Lévy driven continuous-time GARCH process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    3. Francesco Bianchi & Lorenzo Mercuri & Edit Rroji, 2022. "Portfolio Selection with Irregular Time Grids: an example using an ICA-COGARCH(1, 1) approach," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 36(1), pages 57-85, March.
    4. Mercuri, Lorenzo & Perchiazzo, Andrea & Rroji, Edit, 2024. "A Hawkes model with CARMA(p,q) intensity," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 1-26.

    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. Degiannakis, Stavros & Floros, Christos & Dent, Pamela, 2013. "Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence," International Review of Financial Analysis, Elsevier, vol. 27(C), pages 21-33.
    2. 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.
    3. Stavros Degiannakis & Pamela Dent & Christos Floros, 2014. "A Monte Carlo Simulation Approach to Forecasting Multi-period Value-at-Risk and Expected Shortfall Using the FIGARCH-skT Specification," Manchester School, University of Manchester, vol. 82(1), pages 71-102, January.
    4. Chiranjit Dutta & Kara Karpman & Sumanta Basu & Nalini Ravishanker, 2023. "Review of Statistical Approaches for Modeling High-Frequency Trading Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1-48, May.
    5. Asmerilda Hitaj & Lorenzo Mercuri & Edit Rroji, 2019. "Lévy CARMA models for shocks in mortality," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 205-227, June.
    6. Mercuri, Lorenzo & Perchiazzo, Andrea & Rroji, Edit, 2024. "A Hawkes model with CARMA(p,q) intensity," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 1-26.
    7. Peter J. Brockwell & Alexander Lindner, 2021. "Aspects of non‐causal and non‐invertible CARMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 777-790, September.
    8. Louzis, Dimitrios P. & Xanthopoulos-Sisinis, Spyros & Refenes, Apostolos P., 2014. "Realized volatility models and alternative Value-at-Risk prediction strategies," Economic Modelling, Elsevier, vol. 40(C), pages 101-116.
    9. Dimitrios P. Louzis & Spyros Xanthopoulos‐Sisinis & Apostolos P. Refenes, 2013. "The Role of High‐Frequency Intra‐daily Data, Daily Range and Implied Volatility in Multi‐period Value‐at‐Risk Forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(6), pages 561-576, September.
    10. Tan, Shay-Kee & Ng, Kok-Haur & Chan, Jennifer So-Kuen & Mohamed, Ibrahim, 2019. "Quantile range-based volatility measure for modelling and forecasting volatility using high frequency data," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 537-551.
    11. Yildirim, Yavuz & Unal, Gazanfer, 2010. "From Discrete to Continuous: Modeling Volatility of the Istanbul Stock Exchange Market with GARCH and COGARCH," MPRA Paper 27946, University Library of Munich, Germany.
    12. 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.
    13. Louzis, Dimitrios P. & Xanthopoulos-Sisinis, Spyros & Refenes, Apostolos P., 2011. "Are realized volatility models good candidates for alternative Value at Risk prediction strategies?," MPRA Paper 30364, University Library of Munich, Germany.
    14. 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.
    15. Lorenzo Mercuri & Andrea Perchiazzo & Edit Rroji, 2020. "Finite Mixture Approximation of CARMA(p,q) Models," Papers 2005.10130, arXiv.org, revised May 2020.
    16. Francesco Bianchi & Lorenzo Mercuri & Edit Rroji, 2022. "Portfolio Selection with Irregular Time Grids: an example using an ICA-COGARCH(1, 1) approach," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 36(1), pages 57-85, March.
    17. Stefano Iacus & Lorenzo Mercuri, 2015. "Implementation of Lévy CARMA model in Yuima package," Computational Statistics, Springer, vol. 30(4), pages 1111-1141, December.
    18. 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.
    19. Léo Parent, 2022. "The EWMA Heston model," Post-Print hal-04431111, HAL.
    20. Emeka Nkoro & Aham Kelvin Uko, 2016. "Exchange Rate and Inflation Volatility and Stock Prices Volatility: Evidence from Nigeria, 1986-2012," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 6(6), pages 1-4.

    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:jss:jstsof:v:080:i04. 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: Christopher F. Baum (email available below). General contact details of provider: http://www.jstatsoft.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.