The Annals of Statistics

Parameter estimation for infinite variance fractional ARIMA

Piotr S. Kokoszka and Murad S. Taqqu

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Abstract

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

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

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362302

Digital Object Identifier
doi:10.1214/aos/1069362302

Mathematical Reviews number (MathSciNet)
MR1421153

Zentralblatt MATH identifier
0896.62092

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

Keywords
Estimation fractional ARIMA long memory stable distributions heavy tails

Citation

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. https://projecteuclid.org/euclid.aos/1069362302


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