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The relationship between ARIMA-GARCH and unobserved component models with GARCH disturbances

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

Abstract

The objective of this paper is to analyze the consequences of fitting ARIMA-GARCH models to series generated by conditionally heteroscedastic unobserved component models. Focusing on the local level model, we show that the heteroscedasticity is weaker in the ARIMA than in the local level disturbances. In certain cases, the IMA(1,1) model could even be wrongly seen as homoscedastic. Next, with regard to forecasting performance, we show that the prediction intervals based on the ARIMA model can be inappropriate as they incorporate the unit root while the intervals of the local level model can converge to the homoscedastic intervals when the heteroscedasticity appears only in the transitory noise. All the analytical results are illustrated with simulated and real time series.

Suggested Citation

  • Espasa, Antoni & Pellegrini, Santiago & Ruiz, Esther, 2007. "The relationship between ARIMA-GARCH and unobserved component models with GARCH disturbances," DES - Working Papers. Statistics and Econometrics. WS ws072706, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws072706
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    1. King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-933, July.
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    Cited by:

    1. 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.

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    State space models;

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