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

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  • 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
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    References listed on IDEAS

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    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. 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).
    4. Stefano Iacus & Lorenzo Mercuri, 2015. "Implementation of Lévy CARMA model in Yuima package," Computational Statistics, Springer, vol. 30(4), pages 1111-1141, December.
    5. 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.
    6. 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.
    7. 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.
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    Cited by:

    1. 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.
    2. Lorenzo Mercuri & Andrea Perchiazzo & Edit Rroji, 2020. "Finite Mixture Approximation of CARMA(p,q) Models," Papers 2005.10130, arXiv.org, revised May 2020.
    3. 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).

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