Testing For Coefficient Randomness In Local-To-Unity Autoregressions

This study proposes a test for coefficient randomness in autoregressive models where the autoregressive coefficient is local to unity, which is empirically relevant given earlier work. Under this specification, we analyze the effect of the correlation between the random coefficient and disturbance on the properties of tests, a matter that remains largely unexplored in the literature. Our analysis reveals that tests proposed in earlier studies can have poor power when the correlation is moderate to large. The test proposed here is designed to have power functions robust to the correlation. A modified version of the test is suggested that can be applied when the disturbance is serially correlated and conditionally heteroskedastic. The test is shown to have better power properties than existing ones in large and finite samples.