A new method for fuzzification of nested dummy variables by fuzzy clustering membership functions and its application in financial economy

In this study, the aim is to propose a new method for fuzzification of nested dummy variables. The fuzzification idea of dummy variables has been acquired from non-linear part of regime switching models in econometrics. In these models, the concept of transfer functions is like the notion of fuzzy membership functions, but no principle or linguistic sentence have been used for inputs. Consequently, for the non-linear part including transfer function, there is no reason why the different types of functions such as logistic are used. Therefore, in order to solve the aforementioned problem like the regime switching models, the transfer functions are considered for dummy variables. However, the presented transfer functions are proposed by fuzzy clustering membership function. Finally, using fuzzy logic, the membership functions of clusters are combined with each other and constitute the fuzzy nested regimes. The suggested model has been used in financial data of Iran's stock in order to examine the equity premium Puzzle. The results of using above model helped in modeling appropriate second-order moments in consumption capital asset pricing model.