We present a handful of periodogram-based test statistics underneath two statistical procedures that assess the characteristics of a stationary time series in a manner that is similar to the Gromykov et al.(2018) and Ould Haye & Phillippe (2019). We incorporate tapering into these statistics by utilizing a cosine bell taper and a new class of tapers which we term as "random tapers". In the first procedure we test for short memory versus long memory. In the second we test for dependence against the presence of a trend. We demonstrate that under the null, both procedures' limiting distributions are easily obtainable and follow Gamma-like distributions. Moreover, we evaluate the P-value and Empirical Power plots accrued by each test and find that they yield precise results of empirical size. The tests are also implemented into two sets of realworld data and the accrued results are presented.