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 Xt=Φ1Xt−1+…+ΦρXt−ρ+et and we propose a statistic for testing whether or not Φi depends on delayed values Xt−d for some i. We compare the power of our test with that of tests proposed by Luukkonen, Saikkonen and Terasvirta (1988a) and Hjellvik and TjΦstheim (1995) by simulation studies and our test is shown to be satisfactory.