Asymptotic Statistical Theory for Long Memory Volatility Models


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SCHÜTZNER, Martin, 2009. Asymptotic Statistical Theory for Long Memory Volatility Models

@phdthesis{Schutzner2009Asymp-635, title={Asymptotic Statistical Theory for Long Memory Volatility Models}, year={2009}, author={Schützner, Martin}, address={Konstanz}, school={Universität Konstanz} }

<rdf:RDF xmlns:rdf="" xmlns:bibo="" xmlns:dc="" xmlns:dcterms="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:format>application/pdf</dc:format> <dcterms:available rdf:datatype="">2011-03-22T17:45:18Z</dcterms:available> <dc:creator>Schützner, Martin</dc:creator> <dcterms:alternative>Asymptotische statistische Theorie für Volatilitätsmodelle mit langfristigen Abhängigkeiten</dcterms:alternative> <dcterms:rights rdf:resource=""/> <dcterms:title>Asymptotic Statistical Theory for Long Memory Volatility Models</dcterms:title> <dc:date rdf:datatype="">2011-03-22T17:45:18Z</dc:date> <dc:language>eng</dc:language> <dc:contributor>Schützner, Martin</dc:contributor> <dcterms:abstract xml:lang="eng">In this thesis, statistical theory for time series with conditional heteroskedasticity and long memory in volatility is studied. We present appropriate models and consider several problems regarding parametric estimation. First, we discuss the question whether the asymptotic properties of M-estimators of location are affected by slowly decaying autocorrelations in squares. It turns out that under certain symmetry assumptions, consistency and the usual central limit theorem still hold. On the other hand, deviations from these assumptions can lead to non-standard behavior, in particular non-gaussian limiting distributions. For the asymptotic analysis, a connection to Appell polynomials and linear long memory processes is derived. Furthermore, we focus on the parametric LARCH model and investigate a modified conditional maximum likelihood estimator. Consistency and asymptotic normality are derived. The proofs differ substantially from the case of related models such as ARCH($\infty$), since the volatility of a LARCH process is not separated from zero. Moreover, the long memory property leads to additional difficulties, for instance a slower rate of convergence. Consequently, we discuss the question how more efficient estimators can be defined for models with slowly decaying autocorrelations. Therefore, we exploit the result that long memory can be explained by contemporaneous aggregation. Based on a panel scheme of random AR(1) processes, a new estimator for the long memory parameter of the aggregated process is introduced and asymptotic properties are proven. The results indicate that the described procedure could lead to improved statistical methods, in particular for heteroskedastic models with long memory.</dcterms:abstract> <dc:rights>deposit-license</dc:rights> <dcterms:issued>2009</dcterms:issued> <bibo:uri rdf:resource=""/> </rdf:Description> </rdf:RDF>

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