Random simulation method for accuracy test of grey prediction model

The purpose of this paper is to establish a random simulation method to compare the forecasting performance between grey prediction models, and between grey model and other kinds of prediction models. Then, the different performance of three grey models and linear regression prediction model is studied, based on the proposed method.

A random simulation method was proposed to test the modelling accuracy of grey prediction model. This method was enlightened by Monte Carlo simulation method. It regarded a class of sequences as population, and selected a large sample from population though random sampling. Then, sample sequences were modeled by grey prediction model. Through modeling error calculation, the average error of grey model for the sample was obtained. Finally, the grey model accuracy for this kind of problem was acquired by statistical inference testing model. Through the statistical significant test method, the modeling accuracy of grey models for the same problem can be compared. Also, accuracy difference between grey prediction model and regression analysis, support vector machine, neural network, and other forecasting methods can be also compared.

Though random simulation experiments, the following conclusion was obtained. First, grey model can be applied to the long sequence whose growth rate was less than 20 per cent, and the short sequence whose growth rate was less than 50 per cent. Second, GM(1,1) cannot be applied to a long sequence with high growth. Third, growth rate was a more important factor than growth length on modeling accuracy of GM(1,1). Fourth, when the sequence length was short, accuracy of GM(1,1) model was higher than linear regression. While the length of the sequence was more than 15, and the growth rate in [0‐10 per cent], two kinds of modeling error was not significantly different.

The method proposed in the paper can be used to compare the performance of different prediction models, and to select appropriate model for a prediction problem.

The paper succeeded in establishing an accuracy test method for grey models and other prediction models. It will standardize the grey modelling and contribute to application of grey models.