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Minimum distance estimation of possibly non-invertible moving average models
This paper considers estimation of moving average (MA) models with non-Gaussian errors. Information in higher-order cumulants allows identification of the parameters without imposing invertibility. By allowing for an unbounded parameter space, the generalized method of moments estimator of the MA(1) model has classical (root-T and asymptotic normal) properties when the moving average root is inside, outside, and on the unit circle. For more general models where the dependence of the cumulants on the model parameters is analytically intractable, we consider simulation-based estimators with two ...