The finite sample performance is investigated for two versions of the Lagrange multiplier (LM) unit root tests. It is found that the correct size of the augmented tests is obtained at the expense of the power, while the reasonable power of the transformed tests reflects the size distortions...

A test for stationarity in the presence of a structural break is proposed. An unknown break point is endogenously determined at the value minimizing the test statistic. The break point can be estimated reasonably well under the null hypothesis of stationarity, especially when the magnitude of...

It is puzzling that previous studies have found causality only in one direction from sales to advertising, but not the reverse. Employing the sequential causality tests of Toda Phillips (1993), the casual relationship between advertising and sales appears to run in both directions. This finding...

The performance of the Phillips and Perron unit root tests is examined using the optimal bandwidth selection procedure of Andrews and the pre-whitening procedure of Andrews and Monahan. It has been shown that they do not make significant improvements over the tests using fixed truncation lags.