This paper investigates the finite sample properties of likelihood ratio tests for 'stochastic cointegration' that have recently been proposed by S. Johansen and P. Perron and J. Y. Campbell. The author transforms the model into a canonical form and conducts a comprehensive simulation study. He finds that the test performance is very sensitive to the value of the stationary root(s) of the process and to the correlation between the innovations that drive the stationary and nonstationary components of the process. Unfortunately, the simulation results suggest that these asymptotic test procedures are not very powerful for sample sizes that are typical for economic time series.

A limit theory for Wald tests of Granger causality in levels vector autoregressions (VAR's) and error correction models (ECM's) is developed, which allows for stochastic trends and cointegration. Earlier work is extended to the general case, thereby characterizing when these Wald tests are asymptotically valid as 'x'(superscript 2) criteria. Our results for inference from unrestricted levels VAR are not encouraging: the limit theory often involves nuisance parameters and nonstandard distributions, a situation offering no satisfactory statistical basis for these tests. Granger causality tests in ECM's also suffer from nuisance parameter dependencies asymptotically and in some cases nonstandard limit theory. Both these results are somewhat surprising in light of earlier research.