Prediction intervals in conditionally heteroscedastic time series with stochastic components
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Durbin, James & Koopman, Siem Jan, 2001.
"Time Series Analysis by State Space Methods,"
Oxford University Press, number 9780198523543.
- Tom Doan, . "SEASONALDLM: RATS procedure to create the matrices for the seasonal component of a DLM," Statistical Software Components RTS00251, Boston College Department of Economics.
- Doornik, Jurgen A. & Ooms, Marius, 2008. "Multimodality in GARCH regression models," International Journal of Forecasting, Elsevier, vol. 24(3), pages 432-448.
- 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.
- 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.
- 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.
- Broto Carmen & Ruiz Esther, 2009.
"Testing for Conditional Heteroscedasticity in the Components of Inflation,"
Studies in Nonlinear Dynamics & Econometrics,
De Gruyter, vol. 13(2), pages 1-30, May.
- 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.
- Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
- 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.
- 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.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:intfor:v:27:y::i:2:p:308-319. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.