Abstract

In this study, we propose a test for the coefficient randomness in autoregressive models, where the autoregressive coefficient is local to unity. We theoretically show that the correlation between the random coefficient and disturbance crucially affects the power of tests for coefficient randomness and that tests proposed by earlier studies can perform poorly when the degree of the correlation is moderate to large. The test we propose is designed to have a power function robust to the correlation. Because the asymptotic null distribution of the test statistic depends on the correlation between the disturbance and its square, we also propose a modified version of the test statistic such that its asymptotic null distribution is free from this nuisance parameter. The modified test is shown to have better power properties than existing ones in large and finite samples.