Adjusting beliefs via transformed fuzzy returns

Abstract

© 2017 Serials Publications Pvt. Ltd. Change in structural level can cause shifts in the properties of data and, therefore, imposes needs in adjusting belief on the inference. In this study, we consider such a problem in the estimation of financial series. Under Bayesian framework, we propose the idea of combining human approximations and historical observations via transforming fuzzy returns into priors. Fuzzy return has been reintroduced and transformed as an external piece of evidence to the process of Bayesian inference. In addition to the concurrent work [1], this hybrid-prior approach reduces a step of transformation but increases the compatibility with probability theory and, as a result, could be implemented with ease. In our experiment, we selected five samples of financial securities from different markets for examining the proposed methodologies. The problem is multidimensional and analytically intractable but conveniently solved by the Markov-chain Monte-Carlo approximation. Both alternatives have been compared and yielded the quite similar results but traded off in the computational efforts. They indicate the importance on the predictive impacts from expert opinions setting baseline on the commonly-used Maximum Likelihood Estimation method.