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Method of moment estimation in the COGARCH(1,1) model

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  • S. Haug
  • C. Klüppelberg
  • A. Lindner
  • M. Zapp

Abstract

We suggest moment estimators for the parameters of a continuous time GARCH(1,1) process based on equally spaced observations. Using the fact that the increments of the COGARCH(1,1) process are strongly mixing with exponential rate, we show that the resulting estimators are consistent and asymptotically normal. We investigate the empirical quality of our estimators in a simulation study based on the variance gamma driven COGARCH(1,1) model. The estimated volatility with corresponding residual analysis is also presented. Finally, we fit the model to high-frequency data. Copyright Royal Economic Society 2007

Suggested Citation

  • 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.
  • Handle: RePEc:ect:emjrnl:v:10:y:2007:i:2:p:320-341
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    Cited by:

    1. Marín Díazaraque, Juan Miguel & Rodríguez-Bernal, M. T. & Romero, E., 2016. "ABC and Hamiltonian Monte-Carlo methods in COGARCH models," DES - Working Papers. Statistics and Econometrics. WS ws1601, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. repec:eee:intfor:v:34:y:2018:i:1:p:45-63 is not listed on IDEAS
    3. 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.
    4. 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.
    5. 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.
    6. Kallsen Jan & Muhle-Karbe Johannes, 2011. "Method of moment estimation in time-changed Lévy models," Statistics & Risk Modeling, De Gruyter, vol. 28(2), pages 169-194, May.
    7. Rodríguez Bernal, M. T. & Marín Díazaraque, Juan Miguel & 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.
    8. 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.

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