基于遗传算法的ARMA模型定阶新技术

NEW TECHNIQUE FOR DETERMINING THE ORDER OF ARMA MODEL BASED ON GENETIC ALGORITHM

针对时间序列分析与预测中最为常见的ARMA模型的定阶问题,在分析传统定阶方法缺点的基础上,提出了用遗传算法确定ARMA(n,m)模型的自回归阶数n和滑动平均阶数m的新方法。首先由ARMA模型的预测值与实测值定义平均相对变动值(Average relative variance,ARV),并根据其建立遗传算法的适应度函数;然后选取适当的种群数、交叉效、变异率及进化代数;通过逐代进化,得到最优的ARMA模型。最后,通过太阳黑子数据验证了基于遗传算法的ARMA模型定阶新技术的有效性和实用性。

The problem of determining order of ARMA model is aimed at, based on the analysis to disadvantages of traditional approaches, a new method is put forward, which used genetic algorithm (GA) to determine the autoregressive orders n and moving-average orders m in ARMA (n, m) model. Firstly, average relative variance (ARV) is defined according to the value forecasted by ARMA model and the measured value by sensors, in term of which the fitness function for GA is established. Then, the fit parameters for GA such as population, crossover rate, mutation rate, evolved generations are selected. Finally, the optimum ARMA model is obtained after evolved generation by generation. In the end, the sunspot data is used to verify the effectivity and practicability of the new technique for determining the order of ARMA model based on Genetic Algorithm, which is brought forward.