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Fractional ARIMA with stable innovations
Piotr S. Kokoszka
Murad S. Taqqu
Abstract:
We develop the theory of fractionally differenced ARIMA time series with
stable infinite variance innovations establishing conditions for
existence and invertibility. We analyze their
asymptotic dependence structure by means of the codifference and the
covariation, measures
of dependence which are extensions of the covariance and are applicable to
stochastic processes with infinite variance.