Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/44834
Title: On the Finite Dimensional Laws of Threshold GARCH Processes
Authors: Gonçalves, Esmeralda
Leite, Joana
Mendes-Lopes, Nazaré
Issue Date: 2013
Publisher: Springer-Verlag
Abstract: In this chapter we establish bounds for the finite dimensional laws of a threshold GARCH process, X, with generating process Z. In this class of models the conditional standard deviation has different reactions according to the sign of past values of the process. So, we firstly find lower and upper bounds for the law of \left ({X}_{1}^{+},-{X}_{1}^{+},\ldots,{X}_{n}^{+},-{X}_{n}^{+}\right), in certain regions of R^{2n}, and use them to find bounds of the law of \left ({X}_{1},\ldots,{X}_{n}\right). Some of these bounds only depend on the parameters of the model and on the distribution function of the independent generating process, Z. An application of these bounds to control charts for time series is presented.
Peer review: yes
URI: http://hdl.handle.net/10316/44834
DOI: 10.1007/978-3-642-32419-2_24
Publisher Version: https://link.springer.com/chapter/10.1007/978-3-642-32419-2_24
Appears in Collections:I&D CMUC - Livros e Capítulos de Livros

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