Abstract
In the next section the family of stable laws and its properties are introduced. The next section reviews some calibration and simulation methods for stable distributions. Next, a maximum likelihood approach (m.l.e.) is considered under the framework of ARMA processes driven by stable noises. Asymptotic properties are studied and numerical methods are discussed. Finally, we present some simulation results for stable GARCH processes. The Value at Risk (VaR) for these stable models is calculated and compared with its Gaussian counterpart, revealing important differences between them. The procedure is also illustrated in real financial data.
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