Additivity Tests for Nonlinear Autoregression
提出三种检验非线性时间序列中可加性的方法，结合平滑技术与方差分析、拉格朗日乘子检验和置换检验，通过模拟和实例验证其性能。
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.