Trend function hypothesis testing in the presence of serial correlation

TLDR: In this paper, test statistics are proposed that can be used to test hypotheses about the parameters of the deterministic trend function of a univariate time series, and the tests are valid for I(0) and I(1) errors.

Abstract: In this paper test statistics are proposed that can be used to test hypotheses about the parameters of the deterministic trend function of a univariate time series. The tests are valid in the presence of general forms of serial correlation in the errors and can be used without having to estimate the serial correlation parameters either parametrically or nonparametrically. The tests are valid for I(0) and I(1) errors. Trend functions that are permitted include general linear polynomial trend functions that may have breaks at either known or unknown locations. Asymptotic distributions are derived, and consistency of the tests is established. The general results are applied to a model with a simple linear trend. A local asymptotic analysis is used to compute asymptotic size and power of the tests for this example. Size is well controlled and is relatively unaffected by the variance of the initial condition. Asymptotic power curves are computed for the simple linear trend model and are compared to existing tests. It is shown that the new tests have nontrivial asymptotic power. A simulation study shows that the asymptotic approximations are adequate for sample sizes typically used in economics. The tests are used to construct confidence intervals for average GNP growth rates for eight industrialized countries using post-war data.