Identification and validation of periodic autoregressive model with additive noise: finite-variance case
含加性噪声周期自回归模型的识别与验证：有限方差情形AI 解读 ↓
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含加性噪声周期自回归模型的识别与验证：有限方差情形
- 研究问题
- 对于受到有限方差加性噪声扰动的周期自回归数据，如何选择模型阶数、识别周期，并检验拟合后的残差分布？
- 方法与思路
- 作者利用向量残差序列的特征函数获得概率密度，再将其用于信息准则和分布检验，构建阶数、周期选择及验证流程。
- 材料陈述的贡献
- 摘要明确将阶数选择、周期识别和残差分析列为贡献，并提出分析受外部噪声扰动的周期非平稳数据的一般框架。
- 阅读关注点
- 应核对残差特征函数及密度的计算方式、信息准则的具体形式，以及阶数和周期选择如何与另行处理的系数估计衔接。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未经核实；摘要仅提及系数估计而未展开，也未说明选择程序的理论性质与检验表现。
原文摘要
In this paper, we address the problem of modeling data with periodic autoregressive (PAR) time series and additive noise. In most cases, the data are processed assuming a noise-free model (i.e., without additive noise), which is not a realistic assumption in real life. The first two steps in PAR model identification are order selection and period estimation, so the main focus is on these issues. Finally, the model should be validated, so a procedure for analyzing the residuals, which are considered here as multidimensional vectors, is proposed. Both order and period selection, as well as model validation, are addressed by using the characteristic function (CF) of the residual series. The CF is used to obtain the probability density function, which is utilized in the information criterion and for residuals distribution testing. To complete the PAR model analysis, the procedure for estimating the coefficients is necessary. However, this issue is only mentioned here as it is a separate task (under consideration in parallel). The presented methodology can be considered as the general framework for analyzing data with periodically non-stationary characteristics disturbed by finite-variance external noise. The original contribution is in the selection of the optimal model order and period identification, as well as the analysis of residuals. All these findings have been inspired by our previous work on machine condition monitoring that used PAR modeling