This paper presents a new test for the fractional differencing parameter of an ARFIMA model, based on an autoregressive approximation of its short-range component. The test’s behavior is studied using Monte Carlo simulations under a normal distribution and is compared to results found for others well–known long memory tests. In general, the results show that the new test has a superior power while maintaining an adequate size of the test. From the estimation of the fractional differencing parameter using the approximate model, it is possible to identify the correct model for the short–term component, which allows improving the inference on the above mentioned parameter. An additional advantage of the proposed procedure is the possibility of testing long memory in the presence of dependent errors such as in the volatility models of ARCH family. The identification and estimation procedure is applied to simulated data from an ARFIMA–ARCH model.