In this paper, we consider median unbiased estimation of bivariate predictive regression models with non-normal, heavy-tailed or heterescedastic errors. We construct confidence intervals and median unbiased estimator for the parameter of interest. We show that the proposed estimator has better predictive potential than the usual least squares estimator via simulation. An empirical application to finance is given. And a possible extension of the estimation procedure to cointegration models is also described.