A blockwise empirical likelihood method for time series in frequency domain inference
时间序列频域推断的分块经验似然方法AI 解读 ↓
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分类依据与纠错
AI 根据所提供的论文材料归类：摘要直接研究平稳时间序列的周期图、谱参数和频域统计推断。
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时间序列频域推断的分块经验似然方法
- 研究问题
- 如何为平稳弱依赖时间序列的一般谱均值参数构造经验似然推断，突破已有方法对线性过程和比率参数的限制？
- 方法与思路
- 作者结合分块与周期图经验似然，利用谱估计函数和周期图子样本构造谱经验似然，并配套建立 Bootstrap 程序。
- 材料陈述的贡献
- 摘要称，条件下似然比统计量具有卡方极限，可覆盖线性与非线性过程的谱均值参数，并支持渐近有效的区间和检验。
- 阅读关注点
- 应核对弱依赖和谱函数条件、分块与子样本选择、卡方极限及 Bootstrap 的证明范围，以及模拟与实证的比较设置。
- 阅读边界
- 所给为版本未注明的 OpenAlex 索引摘要；所谓温和条件未展开，模拟优势和实证适用性也未给出数值，不能据此保证任意过程下有效。
原文摘要
Frequency domain analysis of time series is often difficult, as periodogram-based statistics involve non-linear averages with complicated variances. Due to the latter, nonparametric approximations from resampling or empirical likelihood (EL) are useful. However, current versions of periodogram-based EL for time series are highly restricted: these are valid only for linear processes and for special parameters (i.e., ratios). For general frequency domain inference with stationary, weakly dependent time series, we develop a spectral EL (SEL) method by combining two previously separate EL frameworks for time series: block-based EL and periodogram-based EL. This hybridization strategy is new and theoretically non-trivial, particularly as existing block-based EL relies on time domain averages that differ substantially from frequency domain counterparts. We formulate SEL statistics for parameters based on spectral estimating functions and periodogram subsamples. Under mild conditions, SEL log-ratio statistics are shown to be well-defined, admitting chi-square limits. Further, we formally establish an effective bootstrap procedure coupled with SEL. As a result, the SEL method can be used for nonparametric, asymptotically correct confidence regions and tests for frequency domain inference without explicit estimation of intricate variances of periodogram-based statistics. This broadly extends the applicability of EL for time series in three directions: (i) SEL can treat any spectral mean parameters; (ii) SEL is valid for both linear and non-linear processes; and (iii) SEL has a provable bootstrap development, which is rare for time series EL, and provides a novel alternative to other resampling approximations in the frequency domain. Simulation studies suggest the proposed method performs well compared to other non-EL approaches. A real data example demonstrates that SEL has application and extension to complicated scenarios.