数据回归中的自回归时间序列误差分位数估计与预测区间有效性研究
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The document "Oracally Efficient Estimation of Innovation Quantile and Prediction Bounds for Autoregressive Time Series" introduces a new estimator for the quantile of autoregressive time series (AR(p)) errors, based on kernel smoothing of Yule-Walker residuals. Under certain assumptions, it is proven that this new estimator is asymptotically efficient for estimating the quantiles using true errors, and therefore has an asymptotically normal distribution. Using this new estimator, prediction intervals for future values of AR(p) are constructed and shown to asymptotically achieve a predetermined confidence level. Extensive data simulation studies validate the theoretical results of the paper, and the proposed method is further illustrated through an application to real-world data. The key words of the paper include AR(p), non-Gaussian distribution, prediction interval, rolling forecast, and Yule-Walker residuals. The author of the paper is Xu Hui, under the guidance of Professor Yang Lijian. This document provides valuable insights and techniques for efficient estimation and prediction of autoregressive time series, with practical implications for various fields.
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