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Prediction intervals in conditionally heteroscedastic time series with stochastic components

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  • Pellegrini, Santiago
  • Ruiz, Esther
  • Espasa, Antoni

Abstract

Differencing is a very popular stationary transformation for series with stochastic trends. Moreover, when the differenced series is heteroscedastic, authors commonly model it using an ARMA-GARCH model. The corresponding ARIMA-GARCH model is then used to forecast future values of the original series. However, the heteroscedasticity observed in the stationary transformation should be generated by the transitory and/or the long-run component of the original data. In the former case, the shocks to the variance are transitory and the prediction intervals should converge to homoscedastic intervals with the prediction horizon. We show that, in this case, the prediction intervals constructed from the ARIMA-GARCH models could be inadequate because they never converge to homoscedastic intervals. All of the results are illustrated using simulated and real time series with stochastic levels.

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Bibliographic Info

Article provided by Elsevier in its journal International Journal of Forecasting.

Volume (Year): 27 (2011)
Issue (Month): 2 (April)
Pages: 308-319

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Handle: RePEc:eee:intfor:v:27:y::i:2:p:308-319

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Web page: http://www.elsevier.com/locate/ijforecast

Related research

Keywords: ARIMA-GARCH models Local level model Nonlinear time series State space models Unobserved component models;

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  1. 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.
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  3. Bowden, Nicholas & Payne, James E., 2008. "Short term forecasting of electricity prices for MISO hubs: Evidence from ARIMA-EGARCH models," Energy Economics, Elsevier, vol. 30(6), pages 3186-3197, November.
  4. Soares, Lacir J. & Medeiros, Marcelo C., 2008. "Modeling and forecasting short-term electricity load: A comparison of methods with an application to Brazilian data," International Journal of Forecasting, Elsevier, vol. 24(4), pages 630-644.
  5. Carmen Broto & Esther Ruiz, 2008. "Testing for conditional heteroscedasticity in the components of inflation," Banco de Espa�a Working Papers 0812, Banco de Espa�a.
  6. Doornik, Jurgen A. & Ooms, Marius, 2008. "Multimodality in GARCH regression models," International Journal of Forecasting, Elsevier, vol. 24(3), pages 432-448.
  7. James H. Stock & Mark W. Watson, 2006. "Why Has U.S. Inflation Become Harder to Forecast?," NBER Working Papers 12324, National Bureau of Economic Research, Inc.
  8. James Payne, 2009. "Inflation targeting and the inflation-inflation uncertainty relationship: evidence from Thailand," Applied Economics Letters, Taylor & Francis Journals, vol. 16(3), pages 233-238.
  9. Harvey, Andrew C & Koopman, Siem Jan, 1992. "Diagnostic Checking of Unobserved-Components Time Series Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 377-89, October.
  10. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543.
  11. Pellegrini, Santiago & Ruiz, Esther & Espasa, Antoni, 2010. "Conditionally heteroscedastic unobserved component models and their reduced form," Economics Letters, Elsevier, vol. 107(2), pages 88-90, May.
  12. James H. Stock & Mark W. Watson, 2007. "Erratum to "Why Has U.S. Inflation Become Harder to Forecast?"," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
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