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Bootstrap prediction intervals for power-transformed time series

  • Pascual, Lorenzo
  • Romo, Juan
  • Ruiz, Esther

In this paper we propose a bootstrap resampling scheme to construct prediction intervals for future values of a variable after a linear ARIMA model has been fitted to a power transformation of it. The advantages over existing methods for computing prediction intervals of power transformed time series are that the proposed bootstrap intervals incorporate the variability due to parameter estimation, and do not rely on distributional assumptions neither on the original variable nor on the transformed one. We show the good behavior of the bootstrap approach versus alternative procedures by means of Monte Carlo experiments. Finally, the procedure is illustrated by analysing three real time series data sets.

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Article provided by Elsevier in its journal International Journal of Forecasting.

Volume (Year): 21 (2005)
Issue (Month): 2 ()
Pages: 219-235

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Handle: RePEc:eee:intfor:v:21:y:2005:i:2:p:219-235
Contact details of provider: Web page: http://www.elsevier.com/locate/ijforecast

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  1. 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, 07.
  2. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-44, April.
  3. Robinson, P M, 1991. "Best Nonlinear Three-Stage Least Squares Estimation of Certain Econometric Models," Econometrica, Econometric Society, vol. 59(3), pages 755-86, May.
  4. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
  5. Harvey, David I. & Newbold, Paul, 2003. "The non-normality of some macroeconomic forecast errors," International Journal of Forecasting, Elsevier, vol. 19(4), pages 635-653.
  6. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 1-29.
  7. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-35, April.
  8. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2001. "Effects of parameter estimation on prediction densities: a bootstrap approach," International Journal of Forecasting, Elsevier, vol. 17(1), pages 83-103.
  9. Sean Collins, 1991. "Prediction techniques for Box-Cox regression models," Finance and Economics Discussion Series 148, Board of Governors of the Federal Reserve System (U.S.).
  10. Foster A. M. & Tian L. & Wei L. J., 2001. "Estimation for the Box-Cox Transformation Model Without Assuming Parametric Error Distribution," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1097-1101, September.
  11. Collins, Sean, 1991. "Prediction Techniques for Box-Cox Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 267-77, July.
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