Local Polynomial Estimation with a FARIMA-GARCH Error Process

Beran, Jan; Feng, Yuanhua

Local Polynomial Estimation with a FARIMA-GARCH Error Process

Files

317_1.pdf(280.28 KB)

Date

1999

Authors

Beran, Jan

Feng, Yuanhua

Series

CoFE-Diskussionspapiere / Zentrum für Finanzen und Ökonometrie; 1999/08

Publication type

Working Paper/Technical Report

Abstract

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.

Subject (DDC)

330 Economics

Keywords

Local Polynimial estimation,FARIMA-GARCH process,semiparametric models

Cite This

ISO 690

BERAN, 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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