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GARCH(1,1) models

Ruprecht-Karls-Universit at HeidelbergFakult at f ur Mathematik und InformatikBachelorarbeitzur Erlangung des akademischen GradesBachelor of Science (B. Sc.) garch (1,1) modelsvorgelegt vonBrandon Williams15. Juli 2011 Betreuung: Prof. Dr. Rainer DahlhausAbstraktIn dieser Bachelorarbeit werden garch (1,1)-Modelle zur Analyse finanzieller Zeitreihen unter-sucht. Dabei werden zuerst hinreichende und notwendige Bedingungen daf ur gegeben, dass solcheProzesse uberhaupt station ar werden k onnen. Danach werden asymptotische Ergebnisse uber rel-evante Sch atzer hergeleitet und parametrische Tests entwickelt.

sive structure within itself. The GARCH(p,q) (generalized ARCH) model is given by X t= e t˙ t ˙2 t = !+ 1X 2 t 1 + :::+ pX 2 t p+ 1˙ 2 t 1 + :::+ q˙ 2 t q: This model, in particular the simpler GARCH(1,1) model, has become widely used in nancial time series modelling and is implemented in most statistics and econometric software packages.

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