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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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  • Pellegrini, Santiago & Ruiz, Esther & Espasa, Antoni, 2011. "Prediction intervals in conditionally heteroscedastic time series with stochastic components," International Journal of Forecasting, Elsevier, vol. 27(2), pages 308-319, April.
    • Handle: RePEc:eee:intfor:v:27:y::i:2:p:308-319
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    1. Christian Francq & Jean-Michel Zakoïan, 2013. "Optimal predictions of powers of conditionally heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 345-367, March.

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