This paper considers the asymptotic properties of some unit root test statistics with the errors belonging to the domain of attraction of a symmetric α-stable law with 0 < α < 2. The results obtained can be viewed as a parallel extension of the asymptotic results for the finite-variance case. The test statistics considered are the Dickey-Fuller, the Lagrange multiplier, the Durbin-Watson and Phillips-type modified. Their asymptotic distributions are expressed as functionals of a standard symmetric α-stable Levy motion. Percentiles of these test statistics are obtained by computer simulation. Asymptotic distributions of sample moments that are part of the test statistics are found to have explicit densities. A small Monte Carlo simulation study is performed to assess small-sample performance of these test statistics for heavy-tailed errors.Stable distributions, Invariance principles, Partial sum processes,

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For a scale mixture of normal vector, X=A 1Â2 G, where X, G # R n and A is a positive variable, independent of the normal vector G, we obtain that the conditional variance covariance, Cov(X 2 | X 1 ), is always finite a.s. for m 2, where X 1 # R n and m

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