Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation

We consider least absolute error estimation in a dynamic nonlinear model with neither independent nor identically distributed errors. The estimator is shown to be consistent and asymptotically normal, with asymptotic covariance matrix depending on the errors through the heights of their density functions at their medians (zero). A consistent estimator of the asymptotic covariance matrix of the estimator is given, and the Wald, Lagrange multiplier, and likelihood ratio tests for linear restrictions on the parameters are discussed. A Lagrange multiplier test for heteroscedasticity based upon the absolute residuals is analyzed. This will be useful whenever the heights of the density functions are related to the dispersions.

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