On tests of trend in a weakly stationary Time Series

Analysis of Time Series is represented by an error model frequently leads to familiar procedures in regression analysis. The statistical models the paper considers are applicable if the underlying population which generates the data has a substantial change in trend at some point. It is intersted in testing hypotheses if this change is significant. Two test statistics are introduced and their distributions are derived under the assumption of weak stationarity. It is proved that these tests are unbiased and their power functions are monotonic. With correlated residuals, their linear test statistic does not give a UMP test. It is shown that a certain quadratic test statistic gives a more powerful test.