On the power of R/S-type tests under contiguous and semi long memory alternatives

The paper deals with the power and robustness of the R/S type tests under contiguous alternatives. We briefly review the long memory models in levels and volatility, and describe the R/S-type tests used to test for the presence of long memory. The empirical power of the tests is investigated when replacing the fractional difference operator (1 - L)d by the mixed operator (1-rL)d in the ARFIMA, LARCH and ARCH time series models. We also investigate the Gegenbauer process with a pole of the spectral density at frequency close to zero.