Sensitivity of OLS estimates against ARFIMA error process as small sample Test for long memory.

Recently there have been much discussion of the theory and applications of long memory processes. In this paper we consider the standard linear model y=X*b+u and assume that the variance covariance matrix of the errors being generated from an ARFIMA(0,d,0) model. Following Banerjee and Magnus (1999) we investigate the sensitivity of the standard OLS slope (B_{L}) and sensitivity of variance estimates (D_{L}) of the linear model near =0. We also investigate the behavior of B_{L} and D_{L} under different short memory specifications (for example AR(1) and MA(1) processes) of u. Recalling the Durbin-Watson statistic (DW or D1) was related to the sensitivity measure for the OLS variance estimate against ARMA(p,q) errors ( Banerjee and Magnus (1999)).This gives us a method to discriminate between long memory and short memory processes, by constructing statistics B_{L/1} and D_{L/1}. In this we interpret D_{L/1} as test for long memory process without the short-memory effects