Bootstrap Speci ̄cation Tests with Dependent Observations and Parameter Estimation Error¤

This paper introduces a bootstrap procedure, accounting for data dependence and parameter estimation error, which facillitates the construction of parametric speci ̄cation tests of di®usion processes. The bootstrap method hinges on a twofold extension of the Politis and Romano (1994) stationary bootstrap. First we provide an empirical process version of this bootstrap, and second, we account for parameter estimation error. In addition to using the bootstrap procedure to form a parameteric di®usion speci ̄cation test, the proposed procedure is used to develop straightforward generalizations of the conditional Kolmogorov test of Andrews (1997) and the conditional mean test of Whang (2000) to the case of dependent observations. One important feature of this new bootstrap is that one need not specify the conditional distribution given the entire history of the process when forming conditional Kolmogorov tests. Hence, the bootstrap, when used to extend Andrews (1997) conditional Kolmogorov test to the case of data dependence, allows for dynamic misspeci ̄cation under both hypotheses. An example based on a version of the Cox, Ingersol and Ross square root process is outlined and related Monte Carlo experiments are carried out. These experiments suggest that the boostrap has excellent ̄nite sample properties, even for samples as small as 500 observations when tests are formed using critical values constructed with as few as 100 bootstrap replications. JEL classi ̄cation: C12, C22.