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Power transformation and threshold modeling for ARCH innovations with applications to tests for ARCH structure

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  • Hwang, S. Y.
  • Kim, Tae Yoon

Abstract

A new class of power-transformed threshold ARCH models is proposed as a threshold-asymmetric generalization of the nonlinear ARCH considered by Higgins and Bera [Internat. Econom. Rev. 33 (1992) 137]. This class is rich enough to include diverse nonlinear and nonsymmetric ARCH models which have been spelled out in the literature. Geometric ergodicity of the model and existence of stationary moments are studied. The model facilitates discussing ARCH structures and hence large sample tests for ARCH structures are investigated via local asymptotic normality approach. Semiparametric tests are also discussed for the case when the error density is unknown.

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  • Hwang, S. Y. & Kim, Tae Yoon, 2004. "Power transformation and threshold modeling for ARCH innovations with applications to tests for ARCH structure," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 295-314, April.
    • Handle: RePEc:eee:spapps:v:110:y:2004:i:2:p:295-314
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    1. Saidi, Youssef & Zakoian, Jean-Michel, 2006. "Stationarity and geometric ergodicity of a class of nonlinear ARCH models," MPRA Paper 61988, University Library of Munich, Germany, revised 2006.
    2. Pan, Jiazhu & Wang, Hui & Tong, Howell, 2008. "Estimation and tests for power-transformed and threshold GARCH models," Journal of Econometrics, Elsevier, vol. 142(1), pages 352-378, January.
    3. Wang, Guochang & Zhu, Ke & Li, Guodong & Li, Wai Keung, 2022. "Hybrid quantile estimation for asymmetric power GARCH models," Journal of Econometrics, Elsevier, vol. 227(1), pages 264-284.
    4. Moosup Kim & Sangyeol Lee, 2019. "Test for tail index constancy of GARCH innovations based on conditional volatility," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 947-981, August.
    5. 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.
    6. Francq, Christian & Zakoian, Jean-Michel, 2013. "Inference in non stationary asymmetric garch models," MPRA Paper 44901, University Library of Munich, Germany.
    7. Boubacar Maïnassara, Y. & Kadmiri, O. & Saussereau, B., 2022. "Estimation of multivariate asymmetric power GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    8. 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.
    9. Guochang Wang & Ke Zhu & Guodong Li & Wai Keung Li, 2019. "Hybrid quantile estimation for asymmetric power GARCH models," Papers 1911.09343, arXiv.org.
    10. Ciccarelli Nicola, 2018. "Semiparametric efficient adaptive estimation of the GJR-GARCH model," Statistics & Risk Modeling, De Gruyter, vol. 35(3-4), pages 141-160, July.
    11. Hwang, S.Y. & Kim, S. & Lee, S.D. & Basawa, I.V., 2007. "Generalized least squares estimation for explosive AR(1) processes with conditionally heteroscedastic errors," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1439-1448, July.
    12. 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.
    13. Aknouche, Abdelhakim & Touche, Nassim, 2015. "Weighted least squares-based inference for stable and unstable threshold power ARCH processes," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 108-115.
    14. Hwang, S.Y. & Basawa, I.V., 2011. "Asymptotic optimal inference for multivariate branching-Markov processes via martingale estimating functions and mixed normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1018-1031, July.
    15. Ciccarelli, Nicola, 2016. "Semiparametric Efficient Adaptive Estimation of the PTTGARCH model," MPRA Paper 72021, University Library of Munich, Germany.

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