Ajuste de cópulas bivariadas via marginal na diagonal

Abstract

It is clear the large number of recent studies about the goodness of fit for copula and undeniable its relevance in various fields, especially in economy. To elect a family of copula to fit a given data set is an important and very complex task and there is not a known method that best suit for this purpose. In recent years, various methods have been proposed observing the different characteristics of the data. The main aim of this paper is to propose two new tests to verify goodness of fit bivariate copulas data via marginal in primary and secondary diagonal. In order to verify the suitability of the tests, the following families of copulas are used: Clayton, Gumbel, Normal and Frank. The calculations are performed with the help of the free software R. In the first test, the marginal in the diagonal, principal and secondary of the copula in study is approached and then chi-square test is performed. The second proposed test verifies if the coefficients of skewness and kurtosis for samples of copulas' families belongs to the confidence interval constructed on the main diagonal and/or secondary diagonal, via Monte Carlo to such. The conclusion is made by checking the control of the rates of errors type I and type II.