Detecting misspecifications in autoregressive conditional duration models and non-negative time-series processes


Yongmiao Hong, Department of Economics and Department of Statistical Science, Uris Hall, Cornell University, Ithaca, NY 14850, USA, and Wang Yanan Institute for Studies in Economics (WISE), and MOE Key Laboratory in Econometrics, Xiamen University, Xiamen 361005, China; Yoon-Jin Lee, Department of Economics, Indiana University, Wylie Hall, Bloomington, IN 47405, USA.


We develop a general theory to test correct specification of multiplicative error models of non-negative time-series processes, which include the popular autoregressive conditional duration (ACD) models. Both linear and nonlinear conditional expectation models are covered, and standardized innovations can have time-varying conditional dispersion and higher-order conditional moments of unknown form. 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 to our context and justify its validity. Simulation studies show that in the context of testing ACD models, finite sample correction gives better sizes in finite samples and are robust to parameter estimation uncertainty. And, it is important to take into account time-varying conditional dispersion and higher-order conditional moments in standardized innovations; failure to do so can cause strong overrejection of a correctly specified ACD model. The proposed tests have reasonable power against a variety of popular linear and nonlinear ACD alternatives.