A piecewise polynomial trend against long range dependence

A sequential testing procedure to distinguish between a piecewise polynomial trend superimposed by short-range dependence and long range dependence is examined. The proposed procedure is based on the local Whittle estimation of long range dependence parameter from the residual series obtained by removing a piecewise polynomial trend. All results are provided with theoretical justifications, and Monte Carlo simulations show that our method achieves good size and provides reasonable power against long range dependence. The proposed method is illustrated to the historical Northern Hemisphere temperature data.