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Titolo: Asymptotics of empirical processes of long memory moving averages with infinite variance
Autore: Koul, HL; Surgailis, D;
 Indirizzi:
 Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA Michigan State Univ E Lansing MI USA 48824 babil, E Lansing, MI 48824 USA
 Titolo Testata:
 STOCHASTIC PROCESSES AND THEIR APPLICATIONS
fascicolo: 2,
volume: 91,
anno: 2001,
pagine: 309  336
 SICI:
 03044149(200102)91:2<309:AOEPOL>2.0.ZU;2W
 Fonte:
 ISI
 Lingua:
 ENG
 Soggetto:
 LINEARREGRESSION MODELS; RANGE DEPENDENT ERRORS; MESTIMATORS; WEAKCONVERGENCE; LIMITTHEOREMS; FUNCTIONALS; SUMS; SEQUENCES; EXPANSION;
 Keywords:
 nonrandom designs; unbounded spectral density; uniform reduction principle; Mestimators;
 Tipo documento:
 Article
 Natura:
 Periodico
 Settore Disciplinare:
 Physical, Chemical & Earth Sciences
 Citazioni:
 37
 Recensione:
 Indirizzi per estratti:
 Indirizzo: Koul, HL Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA Michigan State Univ E Lansing MI USA 48824 Lansing, MI 48824 USA



 Citazione:
 H.L. Koul e D. Surgailis, "Asymptotics of empirical processes of long memory moving averages with infinite variance", STOCH PR AP, 91(2), 2001, pp. 309336
Abstract
This paper obtains a uniform reduction principle for the empirical processof a stationary moving average time series {Xt} with long memory and independent and identically distributed innovations belonging to the domain of attraction of symmetric alpha stable laws, 1 < <alpha> < 2. As a consequence, an appropriately standardized empirical process is shown to converge weakly in the uniformtopology to a degenerate process of the form f Z, whereZ is a standard symmetric <alpha>stable random variable and f is the marginal density of the underlying process. A similar result is obtained for a class of weighted empirical processes. We also show, for a large class of bounded functions h, that the limit law of (normalized) sums Sigma (n)(s=1) h(Xs) is symmetric alpha stable. An application of these results to linear regression models with moving average errors of the above type yields that a large class of Mestimators of regression parameters are asymptoticallyequivalent to the leastsquares estimator and alpha stable. This paper thus extends various wellknown results of DehlingTaqqu and KoulMukherjee from finite variance long memory models to infinite variance models of the above type. (C) 2001 Elsevier Science B.V. All rights reserved. MSC: primary62G05; secondary 62J05; 62E20.
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Documento generato il 24/09/20 alle ore 00:45:28