Bootstrap Specification Tests with Dependent Observations and Parameter Estimation Error

This paper introduces a parametric specification test for dissusion processes which is based on a bootstrap procedure that accounts for data dependence and parameter estimation error. The proposed bootstrap procedure additionally leads to straightforward generalizations of the conditional Kolmogorov test of Andrews (1997) and the conditional mean test of Whang (2000) to the case of dependent observations. The bootstrap 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. 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 misspecification 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 finite 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. .