Fuzzy Regression and the Term Structure of Interest Rates Revisited

Recent articles of Sánchez and Gómez (2003a, 2003b, 2004) addressed the subject of fuzzy regression (FR) and the term structure of interest rates (TSIR). Following Tanaka et. al. (1982), their regression models included a fuzzy output, fuzzy coefficients and an non-fuzzy input vector. The fuzzy components were assumed to be triangular fuzzy numbers (TFNs). The basic idea was to minimize the fuzziness of the model by minimizing the total support of the fuzzy coefficients, subject to including all the given data. Key components of the Sánchez and Gómez methodology included constructing a discount function from a linear combination of splines, the coefficients of which were assumed to be TFNs, and using the minimum and maximum negotiated price of fixed income assets to represent the fuzziness of the dependent variable observations. Given the fuzzy discount functions, the authors provided TFN approximations for the corresponding spot rates and forward rates. The purpose of this article is to revisit the fuzzy regression portions of the foregoing studies, and to discuss issues related to the Tanaka approach, including a consideration of fuzzy least-squares regression models.