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Model checks of higher order time series. (English) Zbl 1094.62117
Summary: We propose and study nonparametric tests for the validity of higher order time-series models. These are based on properly defined residual cusums. In a simulation study it is shown that these tests outperform others when the time series has a dimension reducing character and the dimension becomes large.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
60F17 Functional limit theorems; invariance principles
Software:
Fahrmeir
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