This paper proposes a test statistic for the null hypothesis that a given time series is a stationary long memory process against the alternative hypothesis that it is a¤ected by regime change or a smoothly varying trend. The proposed test is in the frequency domain and is based on the derivatives of the profiled local Whittle likelihood function in a degenerating neighborhood of the origin. The assumptions used are mild, allowing for non-Gaussianity or conditional heteroskedasticity. The resulting null limiting distribution is nuisance parameter free and can be easily simulated. Furthermore, the test is straightforward to implement. In particular, it does not require one to specify the form of the trend or the number of di¤erent regimes under the alternative hypothesis. Monte Carlo simulation shows that the test has decent size and power properties. The paper also considers three empirical applications to illustrate the usefulness of the test.
