Grey–Markov prediction model based on time-continuous Markov model and Levenberg–Marquardt algorithm

Abstract

Grey–Markov model, which combines the advantages of grey system theory and Markov model, has a wide range of applications in various fields. However, reliable predicting can hardly be given for the reason that transition probabilities of traditional Grey–Markov model are obtained by transition frequency with small sample size and the information of small sample size is not fully utilized. To solve this problem, we improve Grey–Markov model based on time-continuous Markov model. First, based on the residual errors of GM (1, 1), we construct the least error square objective function with Kolmogorov forward equations. Second, we improve Levenberg–Marquardt algorithm to obtain the optimal transition intensities and calculate corresponding transition probabilities of Markov model. Third, we obtain predicted value with normal distribution quantile. Not only the improved prediction model has better interpretability, but case study is applied to verify its validity by comparing it with traditional Grey–Markov model.