Powerful Trend Function Tests That are Robustto Strong Serial Correlation with an Applicationto the Prebisch-Singer Hypothesis

In this paper we propose tests for hypotheses regarding the parameters of the deterministictrend function of a univariate time series. The tests do not require knowledge of the form ofserial correlation in the data and they are robust to strong serial correlation. The data cancontain a unit root and the tests still have the correct size asymptotically. The tests we analyzeare standard heteroskedasticity autocorrelation (HAC) robust tests based on nonparametrickernel variance estimators. We analyze these tests using the …xed-b asymptotic frameworkrecently proposed by Kiefer and Vogelsang (2002). This analysis allows us to analyze the powerproperties of the tests with regards to bandwidth and kernel choices. Our analysis shows thatamong popular kernels, there are speci…c kernel and bandwidth choices that deliver tests withmaximal power within a speci…c class of tests. Based on the theoretical results, we proposea data dependent bandwidth rule that maximizes integrated power. Our recommended test isshown to have power that dominates a related test proposed by Vogelsang (1998). We applythe recommended test to the logarithm of a net barter terms of trade series and we …nd thatthis series has a statistically signi…cant negative slope. This …nding is consistent with the wellknown Prebisch-Singer hypothesis.[...]