The Annals of Statistics

Parameter estimation for infinite variance fractional ARIMA

Piotr S. Kokoszka and Murad S. Taqqu

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Consider the fractional ARIMA time series with innovations that have infinite variance. This is a finite parameter model which exhibits both long-range dependence (long memory) and high variability. We prove the consistency of an estimator of the unknown parameters which is based on the periodogram and derive its asymptotic distribution. This shows that the results of Mikosch, Gadrich, Klüppelberg and Adler for ARMA time series remain valid for fractional ARIMA with long-range dependence. We also extend the limit theorem for sample autocovariances of infinite variance moving averages developed in Davis and Resnick to moving averages whose coefficients are not absolutely summable.

Article information

Ann. Statist., Volume 24, Number 5 (1996), 1880-1913.

First available in Project Euclid: 20 November 2003

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E07: Infinitely divisible distributions; stable distributions 62F12: Asymptotic properties of estimators

Estimation fractional ARIMA long memory stable distributions heavy tails


Kokoszka, Piotr S.; Taqqu, Murad S. Parameter estimation for infinite variance fractional ARIMA. Ann. Statist. 24 (1996), no. 5, 1880--1913. doi:10.1214/aos/1069362302.

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