On the probabilistic structure of power threshold generalized arch stochastic processes

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• 作者：E. Gonç ; alves^a ; ^{esmerald@mat.uc.pt} ; J. Leite^b ; N. Mendes-Lopes^a
• 关键词：62G20 ; 62M10
• 刊名：Statistics and Probability Letters
• 出版年：2012
• 出版时间：August, 2012
• 年：2012
• 卷：82
• 期：8
• 页码：1597-1609
• 全文大小：366 K

文摘

The aim of this paper is to develop a probabilistic study on a large and general class of conditionally heteroscedastic models, namely the -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 of those processes is also presented. Finally, the minimal representation of a -TGARCH process is obtained developing, in a unique way, the corresponding conditional moment of order in terms of present and past observations.