On the probabilistic structure of power threshold generalized arch stochastic processes
The aim of this paper is to develop a probabilistic study on a large and general class of conditionally heteroscedastic models, namely the δ-TGARCH processes. For this class of processes we establish necessary and sufficient conditions of strict stationarity, ergodicity and existence of moments. A discussion on the weak stationarity of an associated vectorial process, moments and weak stationarity up to the order δ of those processes is also presented. Finally, the minimal representation of a δ-TGARCH process is obtained developing, in a unique way, the corresponding conditional moment of order δ in terms of present and past observations.
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Volume (Year): 82 (2012)
Issue (Month): 8 ()
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- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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- Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2002. "Stationarity of stable power-GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 97-107, January.
- 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.
- 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.
- Gonçalves, E. & Mendes-Lopes, N., 2010. "On the structure of generalized threshold arch processes," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 573-580, April.
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