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Bootstrap prediction intervals for power-transformed time series

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

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/ijforecast

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References

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  1. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
  2. 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.
  3. 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.
  4. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-35, April.
  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. 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.
  7. 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.
  8. 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.
  9. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-44, April.
  10. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 1-29.
  11. 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.).
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Citations

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Cited by:
  1. Lorenzo Pascual & Esther Ruiz & Diego Fresoli, 2011. "Bootstrap forecast of multivariate VAR models without using the backward representation," Statistics and Econometrics Working Papers ws113426, Universidad Carlos III, Departamento de Estadística y Econometría.
  2. Tommaso Proietti & Helmut Luetkepohl, 2011. "Does the Box-Cox Transformation Help in Forecasting Macroeconomic Time Series?," Economics Working Papers ECO2011/29, European University Institute.
  3. Jan G. de Gooijer & Rob J. Hyndman, 2005. "25 Years of IIF Time Series Forecasting: A Selective Review," Tinbergen Institute Discussion Papers 05-068/4, Tinbergen Institute.
  4. Ng, Jason & Forbes, Catherine S. & Martin, Gael M. & McCabe, Brendan P.M., 2013. "Non-parametric estimation of forecast distributions in non-Gaussian, non-linear state space models," International Journal of Forecasting, Elsevier, vol. 29(3), pages 411-430.
  5. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.

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