A fuzzy Gaussian process regression function approach for forecasting problem

Abstract

A fuzzy regression function approach is a fuzzy inference system method whose rules cannot be determined based on expert opinion, unlike a classical fuzzy inference system. In a fuzzy regression function approach, an input matrix consists of memberships obtained by the fuzzy clustering method and lagged variables of the time series. In the fuzzy regression function approach, the output vector corresponding to this input matrix is also created and the parameter estimation for the method is carried out with the ordinary least square method. As it is known, the ordinary least square method assumes that the data are linear. In addition, although it is very useful to include a priori information describing the formation of the data in the model, in most cases this information is not available. It is also inappropriate to use a model that does not accurately characterize the data. However, it is not appropriate to estimate parameters for nonlinear data using the ordinary least square method. One of the methods to be used in such a situation is the Gaussian process regression method. While the parameters of a selected basis function are fitted in the ordinary least squares regression method, how all measured data are related is determined in the Gaussian process regression. Besides, Gaussian process regression is a Bayesian approach, it can provide uncertainty measurements on forecasts. In this study, a fuzzy Gaussian process regression function is proposed. The contribution of this paper is to propose a new fuzzy inference system that can be used to solve nonlinear data by proposing a fuzzy Gaussian process regression function. The performance of the newly proposed method is evaluated based on the closing values of the Bitcoin and Crude oil time series. The performance comparison of the proposed method is evaluated with many different forecasting methods and it is concluded that the proposed method has superior forecasting performance.