Trend Function Hypothesis Testing in the Presence of Serial Correlation

Test statistics are proposed for testing hypotheses about the parameters of the deterministic trend function of a univariate time series. The tests are valid for general forms of serial correlation in the errors and do not require estimates (parametric or nonparametric) of serial correlation parameters. The tests are valid for stationary and unit root errors. Allowable trend functions include linear polynomials of time that may have structural change. Asymptotic results are applied to a model with a simple linear trend and are used to construct confidence intervals for average GNP growth rates for eight industrialized countries using postwar data.