Testing for neglected nonlinearity in long-memory models

This article 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 approximations and do not restrict the parametric form of the nonlinearity. Some theoretical results for the new tests are obtained, and detailed simulation evidence on the power of the tests is presented. The new methodology is then applied to a wide variety of economic and financial time series.