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Bootstrap prediction intervals in state-space models

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  • Alejandro Rodriguez
  • Esther Ruiz

Abstract

Prediction intervals in state-space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, with the true parameters substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty caused by parameter estimation. Second, the Gaussianity of future innovations assumption may be inaccurate. To overcome these drawbacks, Wall and Stoffer [Journal of Time Series Analysis (2002) Vol. 23, pp. 733-751] propose a bootstrap procedure for evaluating conditional forecast errors that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. In this article, we propose a bootstrap procedure for constructing prediction intervals directly for the observations, which does not need the backward representation of the model. Consequently, its application is much simpler, without losing the good behaviour of bootstrap prediction intervals. We study its finite-sample properties and compare them with those of the standard and the Wall and Stoffer procedures for the local level model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series. Copyright 2009 The Authors. Journal compilation 2009 Blackwell Publishing Ltd

Suggested Citation

  • Alejandro Rodriguez & Esther Ruiz, 2009. "Bootstrap prediction intervals in state-space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(2), pages 167-178, March.
  • Handle: RePEc:bla:jtsera:v:30:y:2009:i:2:p:167-178
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    References listed on IDEAS

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    1. Broto, Carmen & Ruiz, Esther, 2006. "Using auxiliary residuals to detect conditional heteroscedasticity in inflation," DES - Working Papers. Statistics and Econometrics. WS ws060402, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. 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.
    3. Evans, Martin, 1991. "Discovering the Link between Inflation Rates and Inflation Uncertainty," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 23(2), pages 169-184, May.
    4. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, June.
    5. Laurence Ball & Stephen G. Cecchetti, 1990. "Inflation and Uncertainty at Long and Short Horizons," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 21(1), pages 215-254.
    6. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
    7. Cavaglia, Stefano, 1992. "The persistence of real interest differentials: A Kalman filtering approach," Journal of Monetary Economics, Elsevier, vol. 29(3), pages 429-443, June.
    8. Danny Pfeffermann & Richard Tiller, 2005. "Bootstrap Approximation to Prediction MSE for State-Space Models with Estimated Parameters," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 893-916, November.
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    Cited by:

    1. 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.
    2. García-Martos, Carolina & Rodríguez, Julio & Sánchez, María Jesús, 2013. "Modelling and forecasting fossil fuels, CO2 and electricity prices and their volatilities," Applied Energy, Elsevier, vol. 101(C), pages 363-375.
    3. Thiago R. Santos & Glaura C. Franco & Dani Gamerman, 2010. "Comparison of Classical and Bayesian Approaches for Intervention Analysis," International Statistical Review, International Statistical Institute, vol. 78(2), pages 218-239, August.
    4. repec:eme:aecozz:s0731-905320150000035010 is not listed on IDEAS
    5. David Harris & Gael M. Martin & Indeewara Perera & Don S. Poskitt, 2017. "Construction and visualization of optimal confidence sets for frequentist distributional forecasts," Monash Econometrics and Business Statistics Working Papers 9/17, Monash University, Department of Econometrics and Business Statistics.
    6. Lorenzo Boldrini, 2015. "Forecasting the Global Mean Sea Level, a Continuous-Time State-Space Approach," CREATES Research Papers 2015-40, Department of Economics and Business Economics, Aarhus University.
    7. García-Martos, Carolina & Rodríguez, Julio & Sánchez, María Jesús, 2011. "Forecasting electricity prices and their volatilities using Unobserved Components," Energy Economics, Elsevier, vol. 33(6), pages 1227-1239.
    8. Pilar Poncela & Esther Ruiz, 2016. "Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment," Advances in Econometrics,in: Dynamic Factor Models, volume 35, pages 401-434 Emerald Publishing Ltd.
    9. Rodríguez, Alejandro & Ruiz, Esther, 2012. "Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 62-74, January.

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