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 some 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 operator (1–rL) ^d , with r<1 close to 1, in the FARIMA, LARCH and ARCH time series models. We also investigate the Gegenbauer process with a pole of the spectral density at frequency close to zero.