By Pavel Cizek, Wolfgang Karl Hardle, Rafal Weron, Editors
Written in an obtainable and fascinating kind, this self-instructional ebook makes an outstanding use of in depth examples and entire motives. The digital variation, permitting the reader to run, adjust, and increase all quantlets immediate, should be downloaded without charge through the connected license registration card.
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Additional resources for Statistical Tools for Finance and Insurance, 1st Edition
In the ﬁrst step, the models for univariate time series are built for both time series. Here the combined procedure of ARIMA models for conditional mean and GARCH models for conditional variance was used. In the second step, the values of the distribution function for residuals obtained after the application of univariate models were subject to copula analysis. 6 Examples In this example we study three pairs of time series, namely WIG and WIG20, WIG and DJIA, USD/PLN and EUR/PLN. First of all, to get the best ﬁt: an AR(10)-GARCH (1,1) model was built for each component of bivariate time series.
Applications of Copulas for the Calculation of Value-at-Risk, in W. H¨ ardle, T. Kleinow and G. ), Applied Quantitative Finance, Springer. -D. and Thomas, M. (2000). Extreme Value Analysis, in W. H¨ ardle, S. Klinke and M. ), XploRe Learning Guide, Springer. Sklar, A. (1959). Fonctions de repartition a` n dimensions et leurs marges, Publications de l’Institut de Statistique de l’Universit´e de Paris, 8 (1959): 229–231.
In terms of computational speed their method compares favorably to the original method of Koutrouvelis (1980). It has a signiﬁcantly better performance near α = 1 and β = 0 due to the elimination of discontinuity of the characteristic function. However, it returns slightly worse results for very small α. 4 Maximum Likelihood Method The maximum likelihood (ML) estimation scheme for α-stable distributions does not diﬀer from that for other laws, at least as far as the theory is concerned. 16) i=1 where f˜(·; θ) is the stable pdf.
Statistical Tools for Finance and Insurance, 1st Edition by Pavel Cizek, Wolfgang Karl Hardle, Rafal Weron, Editors