On the partial autocorrelation function for locally stationary time series: characterization, estimation and inference
局部平稳时间序列的偏自相关函数：刻画、估计与推断AI 解读 ↓
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局部平稳时间序列的偏自相关函数：刻画、估计与推断
- 研究问题
- 对于具有短程依赖的局部平稳时间序列，如何定义随时间变化的偏自相关函数，并据此估计和检验序列依赖结构？
- 方法与思路
- 作者通过Yule–Walker方程把局部偏自相关联系到最优线性预测系数，用筛方法和最小二乘估计，并提出乘子自助法。
- 材料陈述的贡献
- 摘要称刻画了偏自相关随滞后阶数的衰减及时间平滑性，推广平稳序列的相关检验，并提供算法及R软件包。
- 阅读关注点
- 应核对局部偏自相关定义、预测系数近似误差、筛维度和滞后阶数选择，以及乘子自助法和结构检验的有效条件。
- 阅读边界
- 仅据所给Crossref摘要，不能确认衰减速率及检验条件；摘要部分句子衔接不清，应查阅正文核实近似论述。
原文摘要
SUMMARY For stationary time series, it is common to use plots of the partial autocorrelation function (PACF) or PACF-based tests to explore the temporal dependence structure of the process. To the best of our knowledge, analogues for nonstationary time series have not yet been fully developed. This article aims to fill this gap for locally stationary time series with short-range dependence. First, we characterize the PACF locally in the time domain and show that the jth PACF decays with j at a rate that adapts to the temporal dependence of the time series $ \{x_{i,n}\} $. Second, at each time $ i, $ inspired by Killick et al. (2020). We show that the PACF can be efficiently approximated by the best linear prediction coefficients via the Yule–Walker equations. This allows us to study the PACF via ordinary least squares locally. Third, we show that the PACF is smooth in time for locally stationary time series. We use the sieve method with ordinary least squares to estimate the PACF and construct some statistics to test the PACF and infer the structure of the time series. These tests generalize and modify those used in Brockwell & Davis (1987) for stationary time series. Finally, a multiplier bootstrap algorithm is proposed for practical implementation and an R package Sie2nts is provided to implement the algorithm. Numerical simulations and real-data analysis confirm the usefulness of our results.