Weather Derivatives by Antonis K. Alexandridis & Achilleas D. Zapranis

Author:Antonis K. Alexandridis & Achilleas D. Zapranis
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

5.7.3 Testing Alternative Distributions for the Residuals

In the previous section, the residuals of our proposed model were examined. We concluded that the use of a BM is justified since the normality hypothesis was rejected in only two cities. In order to obtain a better understanding of the distributions of the residuals, we expand our analysis by fitting additional distributions. More precisely, a Lévy family distribution is fitted to the residuals. The Lévy family contains many known distributions as subclasses. To our knowledge, only Benth and Saltyte-Benth (2005) and Bellini (2005) used a Lévy process as the driving noise process. In particular, Benth and Saltyte-Benth (2005) used a generalized hyperbolic distribution. In Bellini (2005), a hyperbolic distribution was used which is a limiting case of the generalized hyperbolic distribution. In this study, two limiting cases of the generalized hyperbolic, the hyperbolic and the NIG, and one limiting case of the Lévy distribution, the stable distribution, are examined.

The generalized hyperbolic probability density function (PDF) is given by

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.