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Kernel smoothed prediction intervals for ARMA models

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  • Klaus Abberger

Abstract

The procedures of estimating prediction intervals for ARMA processes can be divided into model based methods and empirical methods. Model based methods require knowledge of the model and the underlying innovation distribution. Empirical methods are based on the sample forecast errors. In this paper we apply nonparametric quantile regression to the empirical forecast errors using lead time as regressor. With this method there is no need for a distribution assumption. But for the data pattern in this case a double kernel method which allows smoothing in two directions is required. An estimation algorithm is presented and applied to some simulation examples.
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Suggested Citation

  • Klaus Abberger, 2006. "Kernel smoothed prediction intervals for ARMA models," Statistical Papers, Springer, vol. 47(1), pages 1-15, January.
    • Handle: RePEc:spr:stpapr:v:47:y:2006:i:1:p:1-15
    DOI: 10.1007/s00362-005-0269-4
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    References listed on IDEAS

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    1. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-144, April.
    2. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-135, April.
    3. Tsay, Ruey S, 1993. "Calculating Interval Forecasts: Comment: Adaptive Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 140-142, April.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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