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Biometrika 1995 82(2):351-368; doi:10.1093/biomet/82.2.351
© 1995 by Biometrika Trust
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Nonparametric tests of linearity for time series

VIDAR HJELLVIK and DAG TJØSTHEIM

Department of Mathematics, University of Bergen 5007 Bergen, Norway

We introduce tests of linearity for time series based on nonparametric estimates of the conditional mean and the conditional variance. The tests are compared to a number of parametric tests and to nonparametric tests based on the bispectrum. Asymptotic expressions give bad approximations, and the null distribution under linearity is constructed using resampling of the best linear approximation. The new tests perform well on the examples tested.

Key Words: Bootstrap • Conditional mean • Conditional variance • Linear • Nonparametric • Time series


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