Nonparametric Bootstrap Test for Autoregressive Additive Models

Additive autoregressive models are commonly used to describe and simplify the behaviour of a nonlinear time series. When the additive structure is chosen, and the model estimated, it is important to evaluate if it is really suitable to describe the observed data since additivity represents a strong assumption. Although literature presents extensive developments on additive autoregressive models, few are the methods to test additivity which are generally applicable. In this paper a procedure for testing additivity in nonlinear time series analysis is provided. The method is based on: Generalized Likelihood Ratio, Volterra expansion and nonparametric conditional bootstrap (Jianqing and Qiwei, 2003). Investigation on performance (in terms of empirical size and power), and comparisons with other additivity tests proposed by Chen et al. (1995) are made recurring to Monte Carlo simulations.