PREDICTION AND SIGNAL EXTRACTION OF STRONGLY DEPENDENT PROCESSES IN THE FREQUENCY DOMAIN
强依赖过程的频域预测与信号提取AI 解读 ↓
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强依赖过程的频域预测与信号提取
- 研究问题
- 研究基于谱密度典范分解的非参数预测方法能否用于强依赖过程，以及如何从此类过程提取信号。
- 方法与思路
- 作者分析 FLES 在强依赖过程中的性质，并将其改造用于信号恢复；噪声部分仅要求弱依赖而不指定具体模型。
- 材料陈述的贡献
- 摘要称扩展既有预测方法至强依赖过程，并证明所提出信号恢复方法的一致性，形成半参数处理方案。
- 阅读关注点
- 应核对强依赖与噪声弱依赖的定义、谱估计和分解步骤，以及预测性质与信号恢复一致性各自的条件。
- 阅读边界
- Crossref 摘要未说明具体依赖参数、误差界及有限样本比较，不能据其动机认定方法对所有模型误设均稳健。
原文摘要
We frequently observe that one of the aims of time series analysts is to predict future values of the data. For weakly dependent data, when the model is known up to a finite set of parameters, its statistical properties are well documented and exhaustively examined. However, if the model was misspecified, the predictors would no longer be correct. Motivated by this observation and because of the interest in obtaining adequate and reliable predictors, Bhansali (1974, Journal of the Royal Statistical Society, Series B 36, 61–73) examined the properties of a nonparametric predictor based on the canonical factorization of the spectral density function given in Whittle (1963, Prediction and Regulation by Linear Least Squares ) and known as FLES. However, the preceding work does not cover the so-called strongly dependent data. Because of the interest in this type of processes, one of our objectives in this paper is to examine the properties of the FLES for these processes. In addition, we illustrate how the FLES can be adapted to recover the signal of a strongly dependent process, showing its consistency. The proposed method is semiparametric in the sense that, in contrast to other methods, we do not need to assume any particular model for the noise except that it is weakly dependent.