A Multivariable Grey Prediction Model with Fractional-Order Time-Delay Parameters and Its Application

Abstract

Integer-order accumulating generation used by the classical multivariable grey prediction model is unable to adapt to fluctuating sequences and the contemporaneous modeling assumption fails to consider causal time delays between variables. In this paper we construct a fractional-order time-delay multivariable grey prediction model that incorporates fractional-order accumulating generation and multivariable time-delay parameters into one model. Based on it, we propose a collaborative identification strategy for order and time delay, an improved least squares estimation as well as a recursive dynamic parameter adjustment scheme. We have evaluated performance of our model from the three aspects of fitting accuracy, prediction robustness and decomposition of improvement contributions, and defined its applicable conditions. Our model enhances the capability of grey prediction theory for dealing with multivariable sequences with time-delay features.