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Weighted least squares-based inference for stable and unstable threshold power ARCH processes

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  • Aknouche, Abdelhakim
  • Touche, Nassim

Abstract

We establish consistency and asymptotic normality for a weighted least squares estimate (2SWLSE) of a threshold power ARCH process in both stationary and nonstationary environments. For models with heavy tail innovations, the 2SWLSE is more efficient than the quasi-maximum likelihood estimate.

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  • 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.
    • Handle: RePEc:eee:stapro:v:97:y:2015:i:c:p:108-115
    DOI: 10.1016/j.spl.2014.11.011
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    References listed on IDEAS

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    1. 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.
    2. Christian Francq & Jean-Michel Zakoïan, 2013. "Optimal predictions of powers of conditionally heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 345-367, March.
    3. Francq, Christian & Zakoian, Jean-Michel, 2013. "Inference in non stationary asymmetric garch models," MPRA Paper 44901, University Library of Munich, Germany.
    4. Abdelhakim Aknouche, 2012. "Multistage weighted least squares estimation of ARCH processes in the stable and unstable cases," Statistical Inference for Stochastic Processes, Springer, vol. 15(3), pages 241-256, October.
    5. Granger, Clive W.J., 2005. "The past and future of empirical finance: some personal comments," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 35-40.
    6. 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.
    7. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
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    Cited by:

    1. Aknouche Abdelhakim & Demmouche Nacer & Dimitrakopoulos Stefanos & Touche Nassim, 2020. "Bayesian analysis of periodic asymmetric power GARCH models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(4), pages 1-24, September.
    2. Aknouche, Abdelhakim & Demmouche, Nacer & Touche, Nassim, 2018. "Bayesian MCMC analysis of periodic asymmetric power GARCH models," MPRA Paper 91136, University Library of Munich, Germany.
    3. Aknouche, Abdelhakim & Al-Eid, Eid & Demouche, Nacer, 2016. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," MPRA Paper 75770, University Library of Munich, Germany, revised 19 Dec 2016.
    4. Aknouche, Abdelhakim, 2015. "Unified quasi-maximum likelihood estimation theory for stable and unstable Markov bilinear processes," MPRA Paper 69572, University Library of Munich, Germany.
    5. Abdelhakim Aknouche & Eid Al-Eid & Nacer Demouche, 2018. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 485-511, October.

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