This paper constructs tests for the presence of nonlinearity of unknown form in addition to a fractionally integrated, long memory component in a time series process. The tests are based on artificial neural network structures and do not restrict the parametric form of the nonlinearity. The tests only require a consistent estimate of the long memory parameter. Some theoretical results for the new tests are obtained and detailed simulation evidence is also presented on the power of the tests.

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... new methodology is then applied to a wide variety of economic and financial time series. JEL Classification: C22, C12, F31.