TESTING FOR TREND

The paper examines various tests for assessing whether a time series model requires a slope component+ We first consider the simple t-test on the mean of first differences and show that it achieves high power against the alternative hypothesis of a stochastic nonstationary slope and also against a purely deterministic slope+ The test may be modified, parametrically or nonparametrically, to deal with serial correlation+ Using both local limiting power arguments and finite-sample Monte Carlo results, we compare the t-test with the nonparametric tests of Vogelsang ~1998, Econometrica 66, 123–148! and with a modified stationarity test+ Overall the t-test seems a good choice, particularly if it is implemented by fitting a parametric model to the data+ When standardized by the square root of the sample size, the simple t-statistic, with no correction for serial correlation, has a limiting distribution if the slope is stochastic+ We investigate whether it is a viable test for the null hypothesis of a stochastic slope and conclude that its value may be limited by an inability to reject a small deterministic slope+