Evaluating Models of Autoregressive Conditional Duration

This article contains two novelties. First, a unified framework for testing and evaluating the adequacy of an estimated autoregressive conditional duration (ACD) model is presented. Second, two new classes of ACD models, the smooth transition ACD model and the time-varying ACD model, are introduced and their properties discussed. New misspecification tests for the ACD class of models are introduced. These are Lagrange multiplier and Lagrange multiplier–type tests against general forms of additive and multiplicative misspecification of the conditional mean function. These forms include tests against higher-order models, tests of no remaining ACD in the standardized durations, and tests of linearity and parameter constancy. The finite-sample properties of the tests are investigated by simulation. Main statistical properties of the two new classes of ACD models that serve as alternatives in tests of linearity and parameter constancy are investigated. Finally, the tests are applied to ACD models of IBM stock traded at the New York Stock Exchange.