A modified test against spurious long memory

- Detection of spurious long memory can be complicated when the data contains also a truly fractionally integrated component.
- A recent test against spurious long memory by Qu (2011) is modified to improve its finite-sample power properties in this case.
- The modified test builds on prior fractional differencing and offers gains in power while maintaining similar size properties.
- The same critical values can be used as the modified statistic has the same limit distribution as the original test by Qu (2011).

This paper considers the situation where a time series is composed of a fractionally integrated component with long memory parameter d∈(−1/2;1/2) and some contamination in the form of level shifts or trends. The test against spurious long memory by Qu (2011) is consistent in this case as the standard local Whittle estimator for unknown d is upward biased. As demonstrated in this work, the power can be improved by removing the fractional component from the series prior to application of the test. This task can be accomplished by using the modified local Whittle approach by Hou and Perron (2014). This estimator is robust against contaminations and yields nearly unbiased point estimates of d, irrespective of whether contaminations are present or not. The suggested testing procedure has similar size properties as the original test and is often more powerful.