Some copula estimation methods and an application on dependence structure between the Producer Price Index (PPI) and the Consumer Price Index (CPI)

Copulas are the functions which connect one-dimensional margins possessing uniform distribution on the interval to multivariate distribution functions. To put it simply, copulas are used to demonstrate the dependence structure among the random variables. In the recent years, statistical copulas have been studied and their fields of application have been increasing day by day.The purpose of this study is to provide information about several estimation methods which are parametric, non-parametric, semi-parametric, goodness of fit, and is to make sample applications by using some Archimedean copulas. To this end, it is tired to examine the dependence structure between the producer price index (PPI) and the consumer price index (CPI) in the period 1982:01-2011:02 with the 1982 base year of Turkish Statistical Institute (TUIK) through the copula method.In the application section of the third part, non-parametric estimation method, which is considered to be more convenient in application, is examined. Besides, the Kendall Tau scale of association, which allows us to reach the result easily, is used. The relation between the two indexes is analyzed through chi-square test of goodness of fit. According to the results of the test in question, it is seen that the Gumbel-Hougaard copula family explains the dependence structure with parameter between the two indexes.