Frequency domain minimum distance inference for possibly noninvertible and noncausal ARMA models
针对非高斯时间序列，提出一种利用高阶矩信息识别ARMA模型根位置的频域最小距离估计方法，该方法比仅用二阶矩的估计更有效且适用于更一般的模型。
This article introduces frequency domain minimum distance procedures for performing inference in general, possibly non causal and/or noninvertible, autoregressive moving average (ARMA) models. We use information from higher order moments to achieve identification on the location of the roots of the AR and MA polynomials for non-Gaussian time series. We propose a minimum distance estimator that optimally combines the information contained in second, third, and fourth moments. Contrary to existing estimators, the proposed one is consistent under general assumptions, and may improve on the efficiency of estimators based on only second order moments. Our procedures are also applicable for processes for which either the third or the fourth order spectral density is the zero function.