When researchers work on time series or sequence, certain fundamental questions will naturally arise. One of them will be whether the series or sequence exhibits a gradual trend over time. In this thesis, we propose a test statistic based on moving order statistics and establish an exact procedure to test for the presence of monotone trends. We show that the test statistic under the null hypothesis that there is no trend follows the closed skew normal distribution. An efficient algorithm is then developed to generate realizations from this null distribution. A simulation study is conducted to evaluate the proposed test under the alternative hypotheses with linear, logarithmic and quadratic trend functions. Finally, a practical example is provided to illustrate the proposed test procedure.