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

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Author Info

  • Santiago Pellegrini

    ()

  • Esther Ruiz

    ()

  • Antoni Espasa

    ()

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.

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Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws072706.

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Date of creation: Apr 2007
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Handle: RePEc:cte:wsrepe:ws072706

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  1. Mervyn King & Enrique Sentana & Sushil Wadhwani, 1990. "Volatiltiy and Links Between National Stock Markets," NBER Working Papers 3357, National Bureau of Economic Research, Inc.
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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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