Parameter Estimation for In nite Variance Fractional ARIMA
نویسندگان
چکیده
Consider the fractional ARIMA time series with innovations that have innnite variance. This is a nite 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, Kl uppelberg and Adler (1995) for ARMA time series remain valid for fractional ARIMA with long-range dependence. We also extend the limit theorem for sample autocovariances of in-nite variance moving averages developed in Davis and Resnick (1985) to moving averages whose coeecients are not absolutely summable.
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