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Prediction Interval for Autoregressive Time Series via Oracally Efficient Estimation of Multi‐Step‐Ahead Innovation Distribution Function

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  • Juanjuan Kong
  • Lijie Gu
  • Lijian Yang

Abstract

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.

Suggested Citation

  • Juanjuan Kong & Lijie Gu & Lijian Yang, 2018. "Prediction Interval for Autoregressive Time Series via Oracally Efficient Estimation of Multi‐Step‐Ahead Innovation Distribution Function," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(5), pages 690-708, September.
    • Handle: RePEc:bla:jtsera:v:39:y:2018:i:5:p:690-708
    DOI: 10.1111/jtsa.12293
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    Cited by:

    1. Jie Li & Jiangyan Wang & Lijian Yang, 2022. "Kolmogorov–Smirnov simultaneous confidence bands for time series distribution function," Computational Statistics, Springer, vol. 37(3), pages 1015-1039, July.

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