Detecting Misspecifications in Autoregressive Conditional Duration Models via Generalized Spectrum

We propose a class of specification tests for Autoregressive Conditional Duration (ACD) models that are robust to time-varying conditional dispersion and higher order conditional moments of unknown form. Both linear and nonlinear ACD models are covered. No specific estimation method is required, and the tests have a convenient null asymptotic N(0,1) distribution. To reduce the impact of parameter estimation uncertainty in finite samples, we adopt Wooldridge’s (1990a) device and justify its validity. Simulation studies show that the finite sample correction gives better sizes in finite samples and are robust to parameter estimation uncertainty. Also, it is important to take into account time-varying conditional dispersion and higher order conditional moments; failure to do so can cause overrejection of a correctly specified ACD model. The proposed tests have reasonable power against a variety of ACD alternatives.