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.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: $\alpha$-stable distribution; Domain of attraction; Infinite moving average; Linear process; Mixed causal/noncausal process; Nonparametric identification; Unobserved component model.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models

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