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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 16, Fasc. 1,
pages -
 

PREDICTION OF INFINITE VARIANCE FRACTIONAL ARIMA

Piotr S. Kokoszka

Abstract: We establish conditions for the existence and invertibility of fractionally differenced ARIMA time series whose innovations are in the domain of attraction of an a -stable law with a < 2 and consequently have infinite variance. More importantly, we study the effect of truncation on the minimum dispersion linear predictor of X n+k based on the infinite past X ,X ,... n n- 1 We verify that the truncated predictor ^X n+k based on the finite past X ,...,X n 0 is asymptotically efficient, and derive asymptotic bounds on the rate of convergence to 1 of the efficiency of X^ . n+k The bounds are shown to decay like power functions with the rate of decay depending on the index of stability a and the difference parameter d.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

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