The LM type linearity test for STAR nonlinearities is severely distorted when the process is governed by conditional heteroskedasticity. In order to correct the test we propose a parametric bootstrap. It is shown, by means of Monte Carlo methods, that the bootstrap test is almost exact.

Asymptotic tests for fractional integration, such as the Geweke-Porter-Hudak test, the modified rescaled range test and Lagrange multiplier type tests, exhibit size-distortions in small-samples. This paper investigates a parametric bootstrap testing procedure, for size-correction, by means of a...