PREDICTION AND SIGNAL EXTRACTION OF STRONGLY DEPENDENT PROCESSES IN THE FREQUENCY DOMAIN
研究了非参数预测器FLES在强依赖时间序列中的性质，并展示了如何将其用于信号提取，证明了其一致性。该方法无需假设噪声的具体模型，适用于需要可靠预测和信号恢复的场景。
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.