Some asymptotics for long horizon regressions with long memory predictors

We present some asymptotic results for the OLS estimator and for the t-statistic in long horizon regression models with a strongly persistent predictor defined as a long memory process. It is found that the convergence rate for the OLS estimator depends on the memory parameter, and the t-statistic diverges at the rate of square root of T, where T is the sample size. It is then necessary to have the t-test scaled such that it converges to a well-defined limit, which depends on the memory parameters through the functionals on both standard and fractional Wiener processes. The proposed model with fractional processes is attractive in practice as memory parameters are consistently estimable by various methods.