Exploiting fractional accumulation and background value optimization in multivariate interval grey prediction model and its application

In the context of small sample and poor information, the data often change rapidly and interact with multiple factors which make it a challenge to analyse and predict multivariate sequences efficiently. Due to the fact that real systems usually show fractional order characteristics, the aim of this paper is to consider the approach improving the forecast results of multivariate interval grey prediction model via exploiting fractional accumulation. Noting that fractional accumulation could disturb the exponential law, the connotation prediction method is introduced to balance the disturbance. Correspondingly, a fractional connotation prediction method is constructed. In addition, traditional background value coefficient is optimized by using the particle swarm optimization algorithm (PSO). Therefore, a multivariate interval grey fractional accumulative connotation prediction model with optimized background value coefficient is constructed, in which the interval grey number time series are transformed into kernel series and radius series. Finally, the developed model is applied to clean energy prediction in China to verify the feasibility and validity.