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Interest in the interface of nonstationarity and nonlinearity has been increasing in the econometric literature. This paper provides a formal method of testing for nonstationary long memory against the alternative of particular forms of nonlinerarity. The nonlinear models we consider are ESTAR and SETAR models. We provide analysis on the asymptotic properties of the tests and carry out a detailed Monte Carlo study. We find that the tests are in most cases able to dinstinguish between the competing models but in a few cases they are unable to do so raising the prospect that long memory and nonlinear processes may have similar characteristics in small samples.

Testing for Nonstationary Long Memory against Nonlinear Ergodic Models