Publication: The relationship between ARIMA-GARCH and unobserved component models with GARCH disturbances
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2007-04
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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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State space models, Conditional heteroscedasticity, Prediction intervals