This paper proposes a nonparametric test for parametric conditional distributions of dynamic models. The test is of the Kolmogorov type coupled with Khmaladze's martingale transformation. It is asymptotically distribution-free and has nontrivial power against root-n local alternatives. The method is applicable for various dynamic models, including autoregressive and moving average models, generalized autoregressive conditional heteroskedasticity (GARCH), integrated GARCH, and general nonlinear time series regressions. The method is also applicable for cross-sectional models. Finally, we apply the procedure to testing conditional normality and the conditional t-distribution in a GARCH model for the NYSE equal-weighted returns.

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