On the significance testing of fuzzy regression applied to the CAPM: Canadian commodity futures evidence

This paper is written with two congruent objectives. The first is to develop a framework for individual tests of significance of a fuzzy regression model by employing a simple probabilistic estimation procedure. The proposed test, based on two-phase fuzzy regression estimates, is simple and robust. The capital asset pricing model (CAPM), with induction of price limits, serves as the essential component of our analysis, due to its ability to illuminate and determine the risk premiums in a commodity futures market. The second objective is to estimate and test for the significance of the systematic risk of Canadian commodity futures and to illustrate the benefits of the significance testing approach.