依等价AR模型阶次递增的自回归滑动平均模型辨识

Identification of ARMA Models with the Equivalent AR Model Orders Increasing

通过用AR模型等价ARMA模型的思想,提出了一种确定ARMA模型参数估计方法。针对等价AR模型阶次合理选定问题,借助数据乘积矩矩阵的分块矩阵求逆引理,给出了计算等价AR模型参数估计和相应准则函数的依阶次递增递推算法。通过判定准则函数的变化趋势,来确定出AR模型的最合理阶次和相应的参数估计值。然后基于所拟合的AR模型参数,通过解一个不相容代数方程组便可确定ARMA模型参数。仿真实例验证了该算法的性能。

By using AR models to approximate ARMA models, an algorithm is presented for identifying ARMA models. By means of the partition matrix inversion lemma of the data product moment matrix, this paper discusses how to reasonably choose the orders of the equivalent AR models and gives the recursive algorithm of determining the parameter estimates of the AR models and the cost function. By examining the changing rates of the cost function, the reasonable orders and the parameter estimation of the equivalent AR models are determined. Further, the ARMA parameter estimation are obtained by solving a set of algebraic equations involved in the obtained AR model parameters. The simulation results indicate that the proposed algorithms are effective.