A test of linearity against functional coefficient autoregressive models

Our object in this paper is to propose a powerful test for detecting a broad class of nonlinearity of time series as one application of the method by Matsuda (1998). Consider autoregresive models X_t=Φ₁X_t?1+…+Φ_ρX_t?ρ+ε_t and we propose a statistic for testing whether or not Φ_i depends on delayed values X_t?d for some i. We compare the power of our test with that of tests proposed by Luukkonen, Saikkonen and Teräsvirta (1988a) and Hjellvik and TjΦstheim (1995) by simulation studies and our test is shown to be satisfactory.