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Additivity tests for nonlinear autoregression. (English) Zbl 0823.62071

Summary: Additivity is commonly used in the statistical literature to simplify data analysis, especially in analysis of variance and in multivariate smoothing. We propose three procedures for testing additivity in nonlinear time series analysis. The first procedure combines some smoothing techniques with analysis of variance, the second is a Lagrange multiplier test using nonparametric estimation, and the third is a permutation test which uses smoothing techniques to obtain the test statistic and its reference distribution.
We investigate properties of the proposed tests and use simulation to check their performance in finite samples. Applications of the tests to nonlinear time series analysis are discussed and illustrated by real examples.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
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