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Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes

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  • Hwang, S. Y.
  • Basawa, I. V.

Abstract

This article introduces threshold GARCH(1,1) processes to which Box-Cox transformations are applied. This class of processes includes nonlinear ARCH and GARCH models as special cases. The model accommodates asymmetries in conditional variances through a "threshold". The stationary solution is explicitly obtained and moment structures are investigated.

Suggested Citation

  • Hwang, S. Y. & Basawa, I. V., 2004. "Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 209-220, July.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:3:p:209-220
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    Cited by:

    1. Aknouche, Abdelhakim & Al-Eid, Eid M. & Hmeid, Aboubakry M., 2011. "Offline and online weighted least squares estimation of nonstationary power ARCH processes," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1535-1540, October.
    2. Wang, Hui & Pan, Jiazhu, 2014. "Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 117-123.
    3. Haas, Markus, 2009. "Persistence in volatility, conditional kurtosis, and the Taylor property in absolute value GARCH processes," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1674-1683, August.
    4. Lee, Taewook, 2013. "On Jarque–Bera normality and cusum parameter change tests for BCTT-GARCH models," Economics Letters, Elsevier, vol. 119(1), pages 50-54.
    5. Choi, M.S. & Park, J.A. & Hwang, S.Y., 2012. "Asymmetric GARCH processes featuring both threshold effect and bilinear structure," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 419-426.
    6. Carnero M. Angeles & Pérez Ana, 2021. "Outliers and misleading leverage effect in asymmetric GARCH-type models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(1), pages 1-19, February.
    7. Carol Alexander & Emese Lazar, 2009. "Modelling Regime‐Specific Stock Price Volatility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(6), pages 761-797, December.
    8. Qiang Xia & Heung Wong & Jinshan Liu & Rubing Liang, 2017. "Bayesian Analysis of Power-Transformed and Threshold GARCH Models: A Griddy-Gibbs Sampler Approach," Computational Economics, Springer;Society for Computational Economics, vol. 50(3), pages 353-372, October.
    9. Aknouche, Abdelhakim & Demmouche, Nacer & Touche, Nassim, 2018. "Bayesian MCMC analysis of periodic asymmetric power GARCH models," MPRA Paper 91136, University Library of Munich, Germany.
    10. Haas, Markus, 2008. "The autocorrelation structure of the Markov-switching asymmetric power GARCH process," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1480-1489, September.
    11. Park, J.A. & Baek, J.S. & Hwang, S.Y., 2009. "Persistent-threshold-GARCH processes: Model and application," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 907-914, April.
    12. Hwang, S.Y. & Baek, J.S. & Park, J.A. & Choi, M.S., 2010. "Explosive volatilities for threshold-GARCH processes generated by asymmetric innovations," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 26-33, January.
    13. Liu, Ji-Chun, 2007. "Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1428-1438, July.
    14. Liu, Ji-Chun, 2006. "On the tail behaviors of Box-Cox transformed threshold GARCH(1,1) process," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1323-1330, July.

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