Smoothing Transition Autoregressive (STAR) Models with Ordinary Least Squares and Genetic Algorithms Optimization

In this paper we present, propose and examine additional membership functions as also we propose least squares with genetic algorithms optimization in order to find the optimum fuzzy membership functions parameters. More specifically, we present the tangent hyperbolic, Gaussian and Generalized bell functions. The reason we propose that is because Smoothing Transition Autoregressive (STAR) models follow fuzzy logic approach therefore more functions should be tested. Some numerical applications for S&P 500, FTSE 100 stock returns and for unemployment rate are presented and MATLAB routines are provided.