Details

Autor(en) / Beteiligte

• Gouriéroux, Christian

Titel

ARCH Models and Financial Applications [Elektronische Ressource]

Ist Teil von

• Springer Series in Statistics

Ort / Verlag

New York, NY : Springer New York

Erscheinungsjahr

1997

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• 1.1 The DevelopmentofARCH Models Time series models have been initially introduced either for descriptive purposes like prediction and seasonal correction or for dynamic control. In the 1970s, the researchfocusedonaspecificclassoftimeseriesmodels,theso-calledautoregressive moving average processes (ARMA), which were very easy to implement. In thesemodels,thecurrentvalueoftheseriesofinterestiswrittenasalinearfunction ofits own laggedvalues andcurrentandpastvaluesofsomenoiseprocess, which can be interpreted as innovations to the system. However, this approach has two major drawbacks: 1) it is essentially a linear setup, which automatically restricts the type of dynamics to be approximated; 2) it is generally applied without imposing a priori constraintson the autoregressive and moving average parameters, which is inadequatefor structural interpretations. Among the field ofapplications where standard ARMA fit is poorare financial and monetary problems.^
• The financial time series features various forms ofnonlineardynamics,the crucialone being the strongdependenceofthe instantaneous variabilityoftheseriesonitsownpast. Moreover,financial theoriesbasedonconceptslikeequilibriumorrationalbehavioroftheinvestorswouldnaturallysuggest including and testing some structural constraints on the parameters. In this context, ARCH (Autoregressive Conditionally Heteroscedastic) models, introduced by Engle (1982), arise as an appropriate framework for studying these problems. Currently, there existmorethan onehundredpapers and some dozenPh.D. theses on this topic, which reflects the importance ofthis approach for statistical theory, finance and empirical work. 2 1.^
• Introduction From the viewpoint ofstatistical theory, the ARCH models may be considered as some specific nonlinear time series models, which allow for aquite exhaustive studyoftheunderlyingdynamics.Itisthereforepossibletoreexamineanumberof classicalquestions like the random walkhypothesis, prediction intervals building, presenceoflatentvariables [factors] etc., and to test the validity ofthe previously established results