非线性时间序列建模的混合自回归滑动平均模型

Mixed autoregressive moving average model for modeling nonlinear time series

提出了一类用于非线性时间序列建模的混合自回归滑动平均模型(MARMA).该模型是由K个平稳或非平稳的ARMA分量经过混合得到的.讨论了MARMA模型的平稳性条件和自相关函数.给出了MARMA模型参数估计的期望极大化(expectation maximization)算法.运用贝叶斯信息准则(Bayes information criterion)来选择该模型.MARMA模型分布形式富于变化的特征使得它能够对具有多峰分布以及条件异方差的序列进行建模.通过两个实例验证了该模型,并和其他模型进行比较,结果表明MARMA模型能够更好地描述这些数据的特征.

A mixed autoregressive moving average （MARMA） model is proposed for modeling nonlinear time series. The model consists of K stationary or nonstationary ARMA components. The stationary conditions and autocorrelation function of the MARMA process are investigated. The estimation of parameters is easily perfomaed via expectation maximization （EM） algorithrn. The Bayes information criterion （BIC） is used as a tool for the MARMA model selection. The varried feature of conditional distributions of the MARMA model makes it capable of modeling time series with multimodal conditional distributions and with hetero scedasticity. The model is applied to two real data sets and compared with other competing models. The MARMA model appears to capture features of the data better than other competing models do.