Testing for a random walk in random coefficient autoregressive models

W Distaso

Discussion Papers from Department of Economics, University of York

Abstract: New tests for simple unit root and unit root with a possibly nonzero drift processes are proposed, in the context of a random coefficient autoregressive model. The proposed tests are either univariate on the variance of the autoregressive coefficient random variable, or joint on mean and variance. The asymptotic distribution of the tests are derived, and their properties are investigated through a Monte-Carlo simulation experiment. The tests have good power properties. In many cases they perform better than the competing univariate tests available in the literature, despite testing for a multiple joint hypothesis, because the partially one-sided nature is taken into account. In particular, for moderate to large sample sizes, very small values of the variance of the random coefficient variable are needed in order for the tests to reach some power against roots very close to unity. Finally, the proposed tests are applied to the US GDP series.

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