Summary: Many series, such as agricultural commodity prices and economic and financial series, exhibit strong dependence-long memory properties. Since many time series also exhibit seasonal patterns, this paper considers a number of tests, namely U. Hassler’s extension [J. Time Ser. Anal. 14, No. 4, 369–380 (1993; Zbl 0782.62085)] of J. Geweke and S. Porter-Hudak’s [ibid. 4, 221–238 (1983; Zbl 0534.62062)] (GPH) semi-parametric test, Robinson’s frequency domain score test and Silvapulle’s time domain test, to assess the long memory properties of quarterly time series at zero and seasonal frequencies. Very little is known about the finite sample statistical properties of these tests. In a simulation study, we find that time domain and semi-parametric tests generally have rejection rates under the null hypothesis close to the nominal level, with the latter tests’ rejection rates being higher than the nominal level at the semi-annual frequency. In terms of power, the time domain score test was shown to be superior with respect to the others. Establishing the reliability of these tests in finite samples is very useful to applied researchers.