CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
The density of Archimedean copulas and their application for currency rate forecasting
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Read | Akhunzhanov Renat K., Kangina Natalya N., Knyazev Aleksandr G., Lepekhin Oleg A. The density of Archimedean copulas and their application for currency rate forecasting // Caspian journal : management and high technologies. — 2014. — №2. — pp. 10-23. |
Akhunzhanov Renat K. - Ph.D. (Physics and Mathematics), Associate Professor, Astrakhan State University, 20a Tatishchev St., Astrakhan, 414056, Russian Federation, akhunzha@mai.ru
Kangina Natalya N. - Assistant, Astrakhan State University, 20a Tatishchev St., Astrakhan, 414056, Russian Federation, kangina.natali@yandex.ru
Knyazev Aleksandr G. - Ph.D. (Physics and Mathematics), Associate Professor, Astrakhan State University, 20a Tatishchev St., Astrakhan, 414056, Russian Federation, agkniazev@mail.ru
Lepekhin Oleg A. - Ph.D. (Economics), Associate Professor, Astrakhan State University, 20a Tatishchev St., Astrakhan, 414056, Russian Federation, okmb07@yandex.ru
Copula modules of dependence have an important role in applied statistics investigations. For evaluation of the parameters of such models it is necessary to make a definite description of copulas density. This paper observes the definite formulas for density of Kleiton and Franks copulas, and also some recurrent formulas for Gambel-Haugard copulas. The paper refers to some extremal properties of Archimedean copulas density. The copulas refer to the Archimedean copulas which is in demand in applied investigations of the stock market, of the foreign exchange movement, advances portfolio. The paper discusses the practical aspects of implementation of Archimedean copulas density in the frame of the task of forecasting of the currency rate on the example of some foreign currencies (Canadian dollar, British pound, Japanese yen, American dollar, Euro). The results of the imitational modeling showed, that the most forecasting power has the Frank’s copula.
Key words: Archimedean copulas, Clayton copula, Frank copula, Gambel-Haugard copula, density, sequences, recurrent formulas, simulation modeling, forecast, forecasting error, foreign exchange risk management, архимедовы копулы, копула Клейтона, копула Франка, копула