Prediction Interval for Autoregressive Time Series via Oracally Efficient Estimation of Multi‐Step‐Ahead Innovation Distribution Function
提出一种核分布估计方法，基于预测残差估计自回归时间序列多步前向预测误差的分布，进而构建预测区间，并证明其渐近有效性。
A kernel distribution estimator (KDE) is proposed for multi‐step‐ahead prediction error distribution of autoregressive time series, based on prediction residuals. Under general assumptions, the KDE is proved to be oracally efficient as the infeasible KDE and the empirical cumulative distribution function (cdf) based on unobserved prediction errors. Quantile estimator is obtained from the oracally efficient KDE, and prediction interval for multi‐step‐ahead future observation is constructed using the estimated quantiles and shown to achieve asymptotically the nominal confidence levels. Simulation examples corroborate the asymptotic theory.