Sieve Nonparametric Likelihood Methods for Unit Root Tests

This paper develops a new test for a unit root in autoregressive models with serially correlated errors. The test is based on the ``empirical'' Cressie-Read statistic and uses a sieve approximation to eliminate the bias in the asymptotic distribution of the test due to presence of serial correlation. The paper derives the asymptotic distributions of the sieve empirical Cressie-Read statistic under the null hypothesis of a unit root and under a local-to-unity alternative hypothesis. The paper uses a Monte Carlo study to assess the finite sample properties of two well-known members of the proposed test statistic: the empirical likelihood ratio and the Kullback-Liebler distance statistic. The results of the simulations seem to suggest that these two statistics have, in general, similar size and in most cases better power properties than those of standard Augmented Dickey-Fuller tests of a unit root. The paper also analyses the finite sample properties of a sieve bootstrap version of the (square of) the standard Augmented Dickey-Fuller test for a unit root. The results of the simulations seem to indicate that the bootstrap does solve almost completely the size distortion problem, yet at the same time produces a test statistic that has considerably less power than either that of the empirical likelihood or of the Kullback-Liebler distance statistic.