Integrated Conditional Moment Test for Parametric Conditional Distributions

Essay 1: Integrated Conditional MomentTest for Parametric Conditional Distributions (with Herman J. Bierens)This paper extends the Integrated Conditional Moment (ICM) test for the functional form of nonlinear regression models to tests for parametric conditional distributions. This test is formed on the basis of the integrated squared difference between the empirical characteristic function of the actual data and the characteristic function implied by the model. This test is consistent, and has nontrivial power against $sqrt{n}$ -local alternatives.To avoid numerical evaluation of the conditional characteristic function of the model distribution, a simulated integrated conditional moment (SICM) test is proposed, where each theoretical conditional characteristic function is replaced by a simulated counterpart, based on a single random drawing from the corresponding conditional distribution. All the properties of the exact ICM testcarry over to the SICM test.Simulation results show that this method works well. As an empirical application we test the validity of the conditional Poisson distribution for count data, using a health economics related dataset. Our test firmly rejects this model.Essay 2: Integrated Conditional Moment Test forParametric Conditional Distributions of Stationary Time Series Processes (with Herman J. Bierens)In this paper we propose a weighted integrated conditional moment (WICM) test of the validity of parametric specifications of conditional distribution models for stationary time series, by extending the weighted ICM test of Bierens (1984) for time seriesregression models to complete parametric conditional distribution specifications.