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Bootstrap predictive inference for ARIMA processes

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  • Lorenzo Pascual
  • Juan Romo
  • Esther Ruiz

Abstract

In this study, we propose a new bootstrap strategy to obtain prediction intervals for autoregressive integrated moving-average processes. Its main advantage over other bootstrap methods previously proposed for autoregressive integrated processes is that variability due to parameter estimation can be incorporated into prediction intervals without requiring the backward representation of the process. Consequently, the procedure is very flexible and can be extended to processes even if their backward representation is not available. Furthermore, its implementation is very simple. The asymptotic properties of the bootstrap prediction densities are obtained. Extensive finite-sample Monte Carlo experiments are carried out to compare the performance of the proposed strategy vs. alternative procedures. The behaviour of our proposal equals or outperforms the alternatives in most of the cases. Furthermore, our bootstrap strategy is also applied for the first time to obtain the prediction density of processes with moving-average components. Copyright 2004 Blackwell Publishing Ltd.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 25 (2004)
Issue (Month): 4 (07)
Pages: 449-465

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Handle: RePEc:bla:jtsera:v:25:y:2004:i:4:p:449-465

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Cited by:
  1. Jordà, Òscar & Knüppel, Malte & Marcellino, Massimiliano, 2010. "Empirical simultaneous confidence regions for path-forecasts," Discussion Paper Series 1: Economic Studies 2010,06, Deutsche Bundesbank, Research Centre.
  2. Lorenzo Pascual & Juan Romo & Esther Ruiz, 2001. "Bootstrap Prediction Intervals For Power-Transformed Time Series," Statistics and Econometrics Working Papers ws010503, Universidad Carlos III, Departamento de Estadística y Econometría.
  3. Helmut Luetkepohl, 2011. "Vector Autoregressive Models," Economics Working Papers ECO2011/30, European University Institute.
  4. Helmut Lütkepohl, 2010. "Forecasting Aggregated Time Series Variables: A Survey," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing,CIRET, vol. 2010(2), pages 1-26.
  5. Liu, Shen & Maharaj, Elizabeth Ann & Inder, Brett, 2014. "Polarization of forecast densities: A new approach to time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 345-361.
  6. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
  7. Carlos Velasco, 2013. "Comments on: Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(2), pages 237-239, June.
  8. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2006. "Bootstrap prediction for returns and volatilities in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2293-2312, May.
  9. Hee-Young Kim & Yousung Park, 2008. "A non-stationary integer-valued autoregressive model," Statistical Papers, Springer, vol. 49(3), pages 485-502, July.
  10. Alonso, A.M. & Berrendero, J.R. & Hernandez, A. & Justel, A., 2006. "Time series clustering based on forecast densities," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 762-776, November.
  11. Pan, Li & Politis, Dimitris N, 2014. "Bootstrap prediction intervals for linear, nonlinear, and nonparametric autoregressions," University of California at San Diego, Economics Working Paper Series qt67h5s74t, Department of Economics, UC San Diego.
  12. Òscar Jordá & Malte Knuppel & Massimiliano Marcellino, 2012. "Empirical simultaneous prediction regions for path-forecasts," Working Paper Series 2012-05, Federal Reserve Bank of San Francisco.
  13. 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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