Abstract.Two tests are proposed for the hypothesis that data come from an autoregression against the hypothesis that they come from a random coefficient autoregression. The tests are derived from a consideration of theC(α) tests of Neyman, the analysis of tests based on the likelihood ratio being complicated by the fact that the vector of system parameters specified under the null hypothesis lies on the boundary of the parameter space. The asymptotic distributional properties are derived and the powers of the tests compared
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