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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

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Bibliographic Info

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

Volume (Year): 30 (2009)
Issue (Month): 2 (03)
Pages: 167-178

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Handle: RePEc:bla:jtsera:v:30:y:2009:i:2:p:167-178

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  1. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543.
  2. Evans, Martin, 1991. "Discovering the Link between Inflation Rates and Inflation Uncertainty," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 23(2), pages 169-84, May.
  3. 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.
  4. Carmen Broto & Esther Ruiz, 2006. "Using Auxiliary Residuals To Detect Conditional Heteroscedasticity In Inflation," Statistics and Econometrics Working Papers ws060402, Universidad Carlos III, Departamento de Estadística y Econometría.
  5. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  6. 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.
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Cited by:
  1. Jason Ng & Catherine S. Forbes & Gael M. Martin & Brendan P.M. McCabe, 2011. "Non-Parametric Estimation of Forecast Distributions in Non-Gaussian, Non-linear State Space Models," Monash Econometrics and Business Statistics Working Papers 11/11, Monash University, Department of Econometrics and Business Statistics.
  2. 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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