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Multi-Step-Ahead Prediction Intervals for Nonparametric Autoregressions via Bootstrap: Consistency, Debiasing, and Pertinence

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  • Dimitris N. Politis

    (Department of Mathematics and Halicioğlu Data Science Institute, University of California, San Diego, CA 92093, USA)

  • Kejin Wu

    (Department of Mathematics, University of California, San Diego, CA 92093, USA)

Abstract

To address the difficult problem of the multi-step-ahead prediction of nonparametric autoregressions, we consider a forward bootstrap approach. Employing a local constant estimator, we can analyze a general type of nonparametric time-series model and show that the proposed point predictions are consistent with the true optimal predictor. We construct a quantile prediction interval that is asymptotically valid. Moreover, using a debiasing technique, we can asymptotically approximate the distribution of multi-step-ahead nonparametric estimation by the bootstrap. As a result, we can build bootstrap prediction intervals that are pertinent, i.e., can capture the model estimation variability, thus improving the standard quantile prediction intervals. Simulation studies are presented to illustrate the performance of our point predictions and pertinent prediction intervals for finite samples.

Suggested Citation

  • Dimitris N. Politis & Kejin Wu, 2023. "Multi-Step-Ahead Prediction Intervals for Nonparametric Autoregressions via Bootstrap: Consistency, Debiasing, and Pertinence," Stats, MDPI, vol. 6(3), pages 1-29, August.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:3:p:53-867:d:1214875
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    References listed on IDEAS

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    1. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2006. "Bootstrap prediction for returns and volatilities in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2293-2312, May.
    2. Franke, Jurgen & Neumann, Michael H. & Stockis, Jean-Pierre, 2004. "Bootstrapping nonparametric estimators of the volatility function," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 189-218.
    3. Rong Chen & Lijian Yang & Christian Hafner, 2004. "Nonparametric multistep‐ahead prediction in time series analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 669-686, August.
    4. Lorenzo Pascual & Juan Romo & Esther Ruiz, 2004. "Bootstrap predictive inference for ARIMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 449-465, July.
    5. Giordano, Francesco & La Rocca, Michele & Perna, Cira, 2007. "Forecasting nonlinear time series with neural network sieve bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3871-3884, May.
    6. Kejin Wu & Sayar Karmakar, 2021. "Model-Free Time-Aggregated Predictions for Econometric Datasets," Forecasting, MDPI, vol. 3(4), pages 1-14, December.
    7. John. Pemberton, 1987. "Exact Least Squares Multi‐Step Prediction From Nonlinear Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(4), pages 443-448, July.
    8. Dimitris Politis, 2013. "Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 183-221, June.
    9. Manzan, Sebastiano & Zerom, Dawit, 2008. "A bootstrap-based non-parametric forecast density," International Journal of Forecasting, Elsevier, vol. 24(3), pages 535-550.
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