Testing for neglected nonlinearity in long memory models

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. The new methodology is then applied to a wide variety of economic and financial time series.