Specification Testing in Nonlinear Time Series with Long-Range Dependence

This paper proposes a model specification testing procedure for parametric specification of the conditional mean function in a nonlinear time series model with long–range dependence. An asymptotically normal test is established even when long–range dependence is involved. In order to implement the proposed test in practice using a simulated example, a bootstrap simulation procedure is established to find a simulated critical value to compute both the size and power values of the proposed test.