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Motivated by the double autoregressive model with order  p  (DAR( p ) model), in this paper, we study the moving average model with an alternative GARCH error. The model is an extension from DAR( p ) model by letting the order  p  goes to infinity. The quasi maximum likelihood estimator of the parameters in the model is shown to be asymptotically normal, without any strong moment conditions. Simulation results confirm that our estimators perform well. We also apply our model to study a real data set and it has better fitting performance compared to DAR model for the considered data.

Moving Average Model with an Alternative GARCH-Type Error