Chon K H, Korenberg M J, Holstein-Rathlou N H
Department of Molecular Pharmacology, Physiology and Biotechnology, Brown University, Providence, RI 02192, USA.
Ann Biomed Eng. 1997 Sep-Oct;25(5):793-801. doi: 10.1007/BF02684163.
Standard deterministic autoregressive moving average (ARMA) models consider prediction errors to be unexplainable noise sources. The accuracy of the estimated ARMA model parameters depends on producing minimum prediction errors. In this study, an accurate algorithm is developed for estimating linear and nonlinear stochastic ARMA model parameters by using a method known as fast orthogonal search, with an extended model containing prediction errors as part of the model estimation process. The extended algorithm uses fast orthogonal search in a two-step procedure in which deterministic terms in the nonlinear difference equation model are first identified and then reestimated, this time in a model containing the prediction errors. Since the extended algorithm uses an orthogonal procedure, together with automatic model order selection criteria, the significant model terms are estimated efficiently and accurately. The model order selection criteria developed for the extended algorithm are also crucial in obtaining accurate parameter estimates. Several simulated examples are presented to demonstrate the efficacy of the algorithm.
标准确定性自回归移动平均（ARMA）模型将预测误差视为无法解释的噪声源。估计的ARMA模型参数的准确性取决于产生最小的预测误差。在本研究中，开发了一种精确算法，通过使用一种称为快速正交搜索的方法来估计线性和非线性随机ARMA模型参数，其中扩展模型包含预测误差作为模型估计过程的一部分。扩展算法在两步过程中使用快速正交搜索，其中首先识别非线性差分方程模型中的确定性项，然后在包含预测误差的模型中重新估计这些项。由于扩展算法使用正交过程以及自动模型阶数选择标准，因此可以高效且准确地估计重要的模型项。为扩展算法开发的模型阶数选择标准对于获得准确的参数估计也至关重要。给出了几个模拟示例以证明该算法的有效性。
