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信噪比在AR模型定阶方法选择中的研究 被引量:4

Research on Signal-to-Noise Ratio in Order Selection of AR Model
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摘要 AR模型有多种定阶方法,针对特定的时间序列,不同方法得到的结果会有差异,如何适应性地选择合适的定阶方法是一个重要的问题。该文针对低阶自回归模型,在考虑噪声标准差、序列长度和特征根的影响下,引入一种估计模型信噪比的方法,并将其作为评价AIC、BIC和FPE准则定阶准确度的标准.实验表明:当模型的特征根满足|λ1|=|λ2|=…=|λp|=|λmax|时,准确率达到该最大特征根条件下的最大值;定阶准确率与序列长度、特征根相对于单位圆心的距离呈正相关,与噪声标准差无关.在此基础上,提出一种利用参考模型信噪比选择定阶方法的方案,为不同定阶方法优劣的比较提供了新的视角. There are many methods can be used to determine the order of AR models.For specific time series,different method may provide different results.How to select method adaptively for particular series is an important problem,especially in big data era.In this paper,we introduce a method to estimate the signal-to-noise ratio(SNR)of the AR model in low-order noisy environments.It takes the influence of noise standard deviation,series length and eigenvalue of the model into consideration,which can be used as a criterion to evaluate the accuracy of AIC,BIC and FPE.The experimental results show that when the eigenvalue satisfies|λ1|=|λ2|=…=|λp|=|λmax|,the order determination accuracy reaches the maximum under the condition of maximum eigenvalue.The accuracy is positively correlated with the series length and the distance of eigenvalue from origin,independent of noise standard deviation.Finally,based on the experimental results,we can select the order determination method of AR model according to the SNR of converted reference model,which provides a new perspective on the comparison of the advantages and disadvantages in different order determination methods.
作者 王志刚 丁义明 Wang Zhigang;Ding Yiming(Department of Mathematics,School of Sciences,Wuhan University of Technology,Wuhan 430070)
出处 《数学物理学报(A辑)》 CSCD 北大核心 2020年第3期811-823,共13页 Acta Mathematica Scientia
基金 中央高校基本科研业务费专项资金(2017IVA073)。
关键词 自回归模型 信噪比 噪声标准差 序列长度 特征根 参考模型 Autoregressive model Signal-to-noise ratio Noise standard deviation Series length Eigenvalue Reference model
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