## Local Polynomial Estimation with a FARIMA-GARCH Error Process

1999
##### 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.
330 Economics
##### Keywords
Local Polynimial estimation,FARIMA-GARCH process,semiparametric models
##### Cite This
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}
}

RDF
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:bibo="http://purl.org/ontology/bibo/"
xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
xmlns:foaf="http://xmlns.com/foaf/0.1/"
xmlns:void="http://rdfs.org/ns/void#"
xmlns:xsd="http://www.w3.org/2001/XMLSchema#" >
<dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:44:52Z</dcterms:available>
<dc:rights>terms-of-use</dc:rights>
<dc:language>eng</dc:language>
<dcterms:issued>1999</dcterms:issued>
<dcterms:title>Local Polynomial Estimation with a FARIMA-GARCH Error Process</dcterms:title>
<dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
<dc:creator>Beran, Jan</dc:creator>
<dc:contributor>Beran, Jan</dc:contributor>
<dc:format>application/pdf</dc:format>
<dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
<bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/516"/>
<dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/516/1/317_1.pdf"/>
<dc:creator>Feng, Yuanhua</dc:creator>
<foaf:homepage rdf:resource="http://localhost:8080/"/>
<dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:44:52Z</dc:date>
<void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
<dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/516/1/317_1.pdf"/>
<dc:contributor>Feng, Yuanhua</dc:contributor>
<dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
</rdf:Description>
</rdf:RDF>

No