ARCH Models and Financial Applications
Christian Gourieroux
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ARCH Models and Financial Applications

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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-calledautoregres sive 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 e...