A characterization of ARMA and Fractional ARIMA models with infinitely divisible innovations

Details A characterization of ARMA and Fractional ARIMA models with infinitely divisible innovations A characterization of ARMA and Fractional ARIMA models with infinitely divisible innovations

2007-03-25

arxiv.org/abs/math/0703731v1

Mathematics

Statistics Theory

Scientific paper

The object of this paper is to study the asymptotic dependence structure of the linear time series models with infinitely divisible innovations by the use of their characteristic functions. Autoregressive moving-average (ARMA) models and fractional autoregressive integrated moving-average (FARIMA) models are analyzed. As examples of infinitely divisible innovations, the class of radially absolute continuous distributions and general non-symmetric stable distributions are considered. The finite dimensional distributionsn of these models are also obtained.

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