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中文摘要：
研究一类用于非线性时间序列预报的隐多分辨自回归滑动平均（ARMA）模型，该模型以ARMA模型为初始细水平模型（即隐多分辨模型的基本块）．证明了模型的建模精度由水平间的方差决定．研究了新模型的自相关函数结构。给出了参数估计的Bayes方法主Metropolis，Hasting算法．进一步提出了一种可以直接用于不同基本块的隐多分辨模型的非线性时间序列预报方法，证明了其比其他的线性预报方法和隐多分辨模型预报方法降低了预报误差．最后通过数值模拟和实例验证了模型和预报方法，并和其他模型进行比较，结果表明新提出模型和预报方法能够更好地描述数据的特征，提高预报的精度．
英文摘要：
A class of hidden multi-resolution autoregressive moving average （ARMA） model is studied for forecasting nonlinear time series. The model has ARMA model as the original fine level model, that is, the building blocks. The precision of the model for approximating the true one is determined by the variance among the levels. The autocorrelation functions （ACF） structure of the new model is then studied. The estimation of parameters is easily performed via Bayes method and Metropolis-Hasting algorithm. Furthermore, a new method for nonlinear time series forecast is proposed. The method can be directly applied to hidden multi-resolution model with different building blocks, and reduce the forecasting error compared with other linear method and hidden multi-resolution model forecast method. Finally, the model and approaches are illustrated through the use of both simulated and real series. The new model and forecasting method appear to capture features of the data better and provide more precise forecasting than other competing models do.
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