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Prediction intervals in conditionally heteroscedastic time series with stochastic components

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Listed author(s):
  • 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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File URL: http://www.sciencedirect.com/science/article/pii/S0169207010000919
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Article provided by Elsevier in its journal International Journal of Forecasting.

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

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Handle: RePEc:eee:intfor:v:27:y:2011:i:2:p:308-319
DOI: 10.1016/j.ijforecast.2010.05.007
Contact details of provider: Web page: http://www.elsevier.com/locate/ijforecast

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

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