Convergence of Appell Polynomials of Long Range Dependent Moving Averages in Martingale Differences |
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Authors: | Donatas Surgailis Marius Vaičiulis |
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Institution: | (1) Institute of Mathematics and Informatics, Akademijos 4, LT-2600 Vilnius, and;(2) Department of Mathematics, iauliai University, Viinskio 25, LT-5400 iauliai, Lithuania. e-mail;(3) Department of Mathematics, iauliai University, Viinskio 25, LT-5400 iauliai, Lithuania. e-mail |
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Abstract: | We study limit distribution of partial sums SN,k(t) =
s = 1
N t]
Ak(Xs) of Appell polynomials of the long-range dependent moving average process Xt> = i t bt - i i, where {i} is a strictly stationary and weakly dependent martingale difference sequence, and bi id - 1 (0 < d < 1/2). We show that if k(1-2 d)<1, then suitably normalized partial sums SN,k(t) converge in distribution to the kth order Hermite process. This result generalizes the corresponding results of Surgailis, and Avram and Taqqu obtained in the case of the i.i.d. sequence { i}. |
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Keywords: | long memory non-central limit theorem Appell polynomials linear process in martingale differences |
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