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Biometrika 1995 82(2):369-383; doi:10.1093/biomet/82.2.369
© 1995 by Biometrika Trust
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Additivity tests for nonlinear autoregression

RONG CHEN, JUN S. LIU and RUEY S. TSAY

Department of Statistics, Texas A&M University, College Station Texas 77843, U.S.A.
Department of Statistics, Stanford University Stanford, California 94305, U.S.A.
Graduate School of Business, University of Chicago Chicago, Illinois 60637, U.S.A.

Additivity is commonly used in the statistical literature to simplify data analysis, especially in analysis of variance and in multivariate smoothing. In this paper, 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.

Key Words: Alternating conditional expectation • Analysis of variance • Lagrange multiplier test • Permutation test • Tukey's one degree of freedom test


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