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Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models

Donald W. K. Andrews

Abstract

This paper is concerned with the estimation of first-order autoregressive/unit root models with independent identically distributed normal errors. The models considered include those without an intercept, those with an intercept, and those with an intercept and time trend. The autoregressive (AR) parameter $\alpha$ is allowed to lie in the interval $(-1, 1\rbrack$, which includes the case of a unit root. Exactly median-unbiased estimators of the AR parameter $\alpha$ are proposed. Exact confidence intervals for this parameter are introduced. Corresponding exactly median-unbiased estimators and exact confidence intervals are also provided for the impulse response function, the cumulative impulse response, and the half life of a unit shock. An unbiased model selection procedure is discussed. The procedures that are introduced are applied to several data series including real exchange rates, the velocity of money, and industrial production.