A perturbation robust test against spurious long memory

A semiparametric score-type testing procedure to detect spurious long memory under a perturbed fractional framework is proposed. The test statistic is based on the weighted sum of the partial derivatives of the local Whittle with noise estimator. Consistency of the test against the alternatives of smooth trend and random level shift processes is shown. In addition, the limiting distribution of the test is derived. The finite sample properties of the test are examined in a Monte Carlo simulation study. An empirical example on the squared returns and the realised volatilities from the Verizon Communications stock is conducted, and shows the usefulness of the procedure. • Perturbation robust testing to distinguish true long memory from low-frequency contaminated processes. • Deriving the limiting distribution of the test. • Show good finite sample performance. • Solving the puzzle of receiving contradictory results of the DGP of financial volatility processes when using different proxies.