Autoregressive conditionally heteroscedastic (ARCH) models were introduced by Engle in an article published in Econometrica in the early 1980s (Engle, 1982). The proposed application in that article focused on macroeconomic data and one could not imagine, at that time, that the main field of application for these models would be finance. Since the mid-1980s and the introduction of generalized ARCH (or GARCH) models, these models have become extremely popular among both academics and practitioners. GARCH models led to a fundamental change to the approaches used in finance, through an efficient modeling of volatility (or variability) of the prices of financial assets. In 2003, the Nobel Prize for Economics was jointly awarded to Robert F. Engle and Clive W.J. Granger ‘for methods of analyzing economic time series with time™varying volatility (ARCH)’.

Since the late 1980s, numerous extensions of the initial ARCH models have been published (see Bollerslev, 2008, for a (tentatively) exhaustive list). The aim of the present volume is not to review all these models, but rather to provide a panorama, as wide as possible, of current research into the concepts and methods of this field. Along with their development in econometrics and finance journals, GARCH models and their extensions have given rise to new directions for research in probability and statistics. Numerous classes of nonlinear time series models have been suggested, but none of them has generated interest comparable ...

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