When a model is nonlinear, boostrap testing can be expensive because of the need to perform at least one nonlinear estimation for every bootstrap sample. We show that it may be possible to reduce computational costs by performing only a fixed, small number of Newton steps or artificial...

Bootstrap tests are tests for which the significance level is calculated by some sort of bootstrap procedure, which may be parametric or nonparametric. We provide a theoretical framework in which to study the size distorsions of bootstrap P values. We show that, in many circumstances, the size...

This paper employs response surface regressions based on simulation experiments to calculate asymptotic distribution functions of the tests for cointegration proposed by Johansen. The paper provides accurate tables of asymptotic critical values. A program which can be used to calculate both...

We show that, in many circumstances, the size distortion of a bootstrap P value for a test will be one whole order of magnitude smaller than that of the corresponding asymptotic P value. We also show that, at least in the parametric case, the magnitude of the distorsion will depend on the shape...

This paper proposes a new kind of asymmetric GARCh where the conditional variance obeys two different regimes with a smooth transition function. In one formulation variance reacts differently to negative and positive shocks while a second formulation, small and big shocks have separate effects.