Adaptive estimation of cointegrating regressions with ARMA errors

Adaptive maximum likelihood estimators are derived for the parameters of a cointegrating regression whose errors follow a stationary and invertible ARMA process with innovations of unknown distribution. It is shown how to use preliminary estimates of these innovations to nonparametrically estimate their density, which can in turn be used to construct an asymptotically efficient iterative estimator of the cointegrating vector. The asymptotic distribution of this estimator is derived, as are its efficiency gains relative to the Gaussian pseudo-MLE. We evaluate the finite sample behaviour of the estimator through a small Monte Carlo experiment, and report the results of an empirical application to the foreign exchange market.