The variable weighted functions of combined forecasting

In this paper, we describe a mathematical framework to determine the weighted functions in variable weight combined forecasting (VWCF) problems with continuous variable weights. Due to the polynomial approximation theorem and matrix analysis, the general formula of the variable weighted functions wi(t) in the VWCF problems is obtained. We put forward the optimal weighted matrix and get the optimal weights by minimizing errors square sum J at any given times.