Finite sample bias of the least squares estimator in an AR(p) model: estimation, inference, simulation and examples

This paper shows that the first order bias of least squares estimators of the coefficients of an AR(p) model is important for 'typical' macroeconomic time series and proposes a simple to apply method of bias reduction. Biases in individual coefficients often cumulate in the sum with far-reaching consequences for the cumulative impulse response function. This function, being nonlinear in the underlying coefficients, is particularly sensitive to biases when, as is often the case, the shocks are long-lived. Simulations and examples demonstrate some of the magnitudes involved.