On the probabilistic structure of power threshold generalized arch stochastic processes

E. Gonçalves, J. Leite and N. Mendes-Lopes

Statistics & Probability Letters, 2012, vol. 82, issue 8, 1597-1609

Abstract: 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.

Keywords: Power TGARCH models; Minimal representation; Stationarity; Ergodicity; Stationarity up to order δ (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2012.04.014

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