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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.

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
    DOI: 10.1111/j.1467-9892.2008.00604.x
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    1. Broto, Carmen, 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.
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    Cited by:

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    8. 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.
    9. 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.
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