ARMA建模的有约束最小二乘拟合方法

本文分析了以前ARMA建模中的一些方法。这些方法只用到相关序列的一部分。对于没有误差的ARMA序列来说,这样做是充分的,因为ARMA过程的信息已经全部包含在其相关序列的一部分中。但是对实测的相关序列,我们可以利用相关序列的全部来减小误差对参数估计的影响。另外,这些方法在实际上还不能保证得到的谱估计是非负的。基于上述考虑,本文提出了一种有约束的最小二乘拟合方法。该方法利用实测相关序列的全体,并且保证得到的谱估计是非负的。

A CONSTRAINED LEAST SQUARES FITTING TECHNIQUE FOR ARMA MODELING

Several ARMA modeling approaches are addressed. In these methods only part of the correlation sequence is employed for estimating parameters. It is satisfying if the given correlation sequence is of real ARMA, since an ARMA process can be completely determined by part of its correlation sequence. But for case of measured correlation sequence the whole sequence may be used to reduce the effect of error on model parameter estimation. In addition, these methods now do not guarantee a nonnegative spectral estimate. In view of the above mentioned fact, a constrained least squares fitting technique is proposed which utilizes the wlole measured correlation sequence and guarantees a nonnegative estimate.