Nonparametric model checks for time series

@inproceedings{Koul1999NonparametricMC,
  title={Nonparametric model checks for time series},
  author={Hira L. Koul and Winfried Stute},
  year={1999}
}
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. 

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