Logistic-Grey-Markov prediction model

Purpose In this study, a novel grey combined model, termed the logistic-Grey-Markov model, is proposed. This model aims to construct a relation function between transition probabilities and residual errors and fully utilize the information from residual errors to calculate optimal transition probabilities for more accurate predictions. Design/methodology/approach To address this issue, the logistic function is introduced and improved to accommodate different types of samples. Then the improved logistic function is applied to construct a relation function between transition probabilities and sample residual errors. Additionally, to obtain the optimal coefficients in the relation function, a least square objective function is constructed, and the Levenberg–Marquardt algorithm is employed. With these optimal coefficients, the relation function can fully utilize the information of residual errors and calculate the optimal transition probabilities. Findings The improved logistic function in the logistic-Grey-Markov model ensures that the information from sample residual errors is fully utilized and case studies demonstrate that the proposed logistic-Grey-Markov model can effectively improve the prediction accuracy. Originality/value One of the strengths of the Grey-Markov model is its ability to predict outcomes with small and highly volatile samples. However, the prediction accuracy is not ideal due to the information waste of residual errors, especially when only a small sample size is available. The proposed logistic-Grey-Markov model can fully utilize the information in residual errors to calculate the optimal transition probabilities and improve the accuracy of the Grey-Markov model.