Predictive regression: An improved augmented regression method

• This paper proposes three modifications to the augmented regression method.
• These modifications include improved bias-correction and stationarity-correction.
• The matrix formula is introduced for covariance matrix estimation.
• It is found that these modifications deliver substantial gain in small samples.
• The improved method is applied to monthly US dividend yield and stock return.

This paper proposes three modifications to the augmented regression method (ARM) for bias-reduced estimation and statistical inference in the predictive regression. They are in relation to improved bias-correction, stationarity-correction, and the use of matrix formulae for bias-correction and covariance matrix estimation. The improved ARM parameter estimators are unbiased to the order of n− 1, and always satisfy the condition of stationarity. With the matrix formulae, the improved ARM can easily be implemented for a high order model with multiple predictors. From an extensive Monte Carlo experiment, it is found that the improved ARM delivers substantial gain in parameter estimation, statistical inference, and out-of-sample forecasting in small samples. As an application, the improved ARM is applied to monthly US stock return data to evaluate the predictive power of dividend yield in univariate and bivariate predictive models.