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Bootstrap prediction intervals for power-transformed time series

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  • Pascual, Lorenzo
  • Romo, Juan
  • Ruiz Ortega, 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.

Suggested Citation

  • Pascual, Lorenzo & Romo, Juan & Ruiz Ortega, Esther, 2001. "Bootstrap prediction intervals for power-transformed time series," DES - Working Papers. Statistics and Econometrics. WS ws010503, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws010503
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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. 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.
    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. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
    6. Collins, Sean, 1991. "Prediction Techniques for Box-Cox Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 267-277, July.
    7. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 1-29.
    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. 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.
    11. Robinson, P M, 1991. "Best Nonlinear Three-Stage Least Squares Estimation of Certain Econometric Models," Econometrica, Econometric Society, vol. 59(3), pages 755-786, May.
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    Cited by:

    1. Proietti, Tommaso & Lütkepohl, Helmut, 2013. "Does the Box–Cox transformation help in forecasting macroeconomic time series?," International Journal of Forecasting, Elsevier, vol. 29(1), pages 88-99.
    2. Olave-Rojas, David & Álvarez-Miranda, Eduardo, 2021. "Towards a complex investment evaluation framework for renewable energy systems: A 2-level heuristic approach," Energy, Elsevier, vol. 228(C).
    3. Ruiz Ortega, Esther & Fresoli, Diego Eduardo & Pascual, Lorenzo, 2011. "Bootstrap forecast of multivariate VAR models without using the backward representation," DES - Working Papers. Statistics and Econometrics. WS ws113426, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Felix Wick & Ulrich Kerzel & Martin Hahn & Moritz Wolf & Trapti Singhal & Daniel Stemmer & Jakob Ernst & Michael Feindt, 2021. "Demand Forecasting of Individual Probability Density Functions with Machine Learning," SN Operations Research Forum, Springer, vol. 2(3), pages 1-39, September.
    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.
    6. Gloria Gonzalez‐Rivera & Yun Luo & Esther Ruiz, 2020. "Prediction regions for interval‐valued time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 373-390, June.
    7. Trucíos, Carlos & Hotta, Luiz K., 2016. "Bootstrap prediction in univariate volatility models with leverage effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 91-103.
    8. 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.
    9. 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.
    10. Ahmed, Wajid Shakeel & Sheikh, Jibran & Ur-Rehman, Kashif & Shafi, khuram & Shad, Shafqat Ali & Butt, Faisal Shafique, 2020. "New continuum of stochastic static forecasting model for mutual funds at investment policy level," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    11. David Olave-Rojas & Eduardo Álvarez-Miranda & Alejandro Rodríguez & Claudio Tenreiro, 2017. "An Optimization Framework for Investment Evaluation of Complex Renewable Energy Systems," Energies, MDPI, vol. 10(7), pages 1-26, July.

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