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Nonparametric model checks for time series. (English) Zbl 0955.62089
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 the 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.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
62M30 Inference from spatial processes
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