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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:
0304-4149(200102)91:2<309:AOEPOL>2.0.ZU;2-W
Fonte:
ISI
Lingua:
ENG
Soggetto:
LINEAR-REGRESSION MODELS; RANGE DEPENDENT ERRORS; M-ESTIMATORS; WEAK-CONVERGENCE; LIMIT-THEOREMS; FUNCTIONALS; SUMS; SEQUENCES; EXPANSION;
Keywords:
non-random designs; unbounded spectral density; uniform reduction principle; M-estimators;
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. 309-336

Abstract

This paper obtains a uniform reduction principle for the empirical processof a stationary moving average time series {X-t} 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 uniform-topology 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(X-s) 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 M-estimators of regression parameters are asymptoticallyequivalent to the least-squares estimator and alpha -stable. This paper thus extends various well-known results of Dehling-Taqqu and Koul-Mukherjee 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