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Bootstrap prediction intervals for power-transformed time series

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  • Pascual, Lorenzo

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, 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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    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, July.
    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. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
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    7. 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.
    8. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-135, April.
    9. 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.
    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. 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.
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    Cited by:

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    2. 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.
    3. 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).
    4. 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.
    5. Gloria Gonzalez-Rivera & Yun Luo & Esther Ruiz, 2018. "Prediction Regions for Interval-valued Time Series," Working Papers 201817, University of California at Riverside, Department of Economics.
    6. 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).
    7. Pascual, Lorenzo & Fresoli, Diego Eduardo, 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.
    8. 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.
    9. 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.
    10. 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.
    11. Jan G. De Gooijer & Rob J. Hyndman, 2005. "25 Years of IIF Time Series Forecasting: A Selective Review," Monash Econometrics and Business Statistics Working Papers 12/05, Monash University, Department of Econometrics and Business Statistics.
    12. 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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