A Test Against Spurious Long Memory

Abstract

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 of short memory, affected 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. 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 different 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.

Keywords: structural change, trend, fractional integration, semiparametric, frequency domain estimates

JEL Classification: C12, C22