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On uniqueness of moving average representations of heavy-tailed stationary processes

Gouriéroux, Christian and Zakoian, Jean-Michel (2014): On uniqueness of moving average representations of heavy-tailed stationary processes.

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Abstract

We prove the uniqueness of linear i.i.d. representations of heavy-tailed processes whose distribution belongs to the domain of attraction of an $\alpha$-stable law, with $\alpha<2$. This shows the possibility to identify nonparametrically both the sequence of two-sided moving average coefficients and the distribution of the heavy-tailed i.i.d. process.

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