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On Uniqueness of Moving Average Representations of Heavy‐tailed Stationary Processes
Author(s) -
Gouriéroux Christian,
Zakoïan JeanMichel
Publication year - 2015
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12139
Subject(s) - mathematics , uniqueness , sequence (biology) , moving average , distribution (mathematics) , stable distribution , stationary process , stationary sequence , heavy tailed distribution , gaussian , identification (biology) , statistical physics , attraction , mathematical analysis , statistics , stochastic process , genetics , physics , botany , quantum mechanics , biology , linguistics , philosophy
The paper solves the open problem of identification of two‐sided moving average representations with i.i.d. summands, for stationary processes in non‐Gaussian domains of attraction of α ‐stable laws. This shows the possibility to identify nonparametrically both the sequence of two‐sided moving average coefficients and the distribution of the underlying heavy‐tailed i.i.d. process.