In this paper test statistics are proposed that can be used to test for shifts in the 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 both I(0) and I(1) errors. The tests are designed to detect a single break at a known or unknown date. Asymptotic distributions are tabulated. A local asymptotic analysis is used to evaluate the size and power of the tests. Local asymptotic power indicates that the new tests have nontrivial asymptotic power. If the supremum statistic is used when the break date is unknown, one of the new tests has greater power than currently available statistics. Simulations are used to assess the finite sample size and power of the tests. A discussion is given on computing confidence intervals for trend function parameters when there is a trend shift at an unknown date. Such confidence intervals are computed for GNP growth rates of 16 countries using historical data.
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