Local Polynomial Estimation with a FARIMA-GARCH Error Process

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1999
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This paper considers a class of semiparametric models being the sum of a nonparametric trend function g and a FARIMA-GARCH error process. Estimation of g (v) , the vth derivative of g, by local polynomial fitting is investigated. The focus is on the derivation of the asymptotic normality of g (v) . At first a central limit theorem based on martingale theory is developed and asymptotic normality of the sample mean of a FARIMA-GARCH process is proved. The central limit theorem is then extended from the case of an unweighted sum to a weighted sum in order to show the asymptotic normality of g(v) . As an auxiliary result, the weak consistency of a weighted sum is obtained for sec- ond order stationary time series with short- or long memory under very weak conditions. Asymptotic results on g(v) in the presentation of long memory as well as antipersistence are also given for the current model.

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330 Wirtschaft
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Local Polynimial estimation, FARIMA-GARCH process, semiparametric models
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ISO 690BERAN, Jan, Yuanhua FENG, 1999. Local Polynomial Estimation with a FARIMA-GARCH Error Process
BibTex
@techreport{Beran1999Local-516,
  year={1999},
  series={CoFE-Diskussionspapiere / Zentrum für Finanzen und Ökonometrie},
  title={Local Polynomial Estimation with a FARIMA-GARCH Error Process},
  number={1999/08},
  author={Beran, Jan and Feng, Yuanhua}
}
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