Nonparametric model checks for time series

This paper studies a class of tests useful for testing the goodness-of-fit of an autoregressive model. These tests are based on a class of empirical processes marked by certain residuals. The paper first gives their large sample behavior under null hypotheses. Then a martingale transformation of the underlying process is given that makes tests based on it asymptotically distribution free. Consistency of these tests is also discussed briefly.